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physics/9403001
|
Desperately Seeking Superstrings
|
We provide a detailed analysis of the problems and prospects of superstring
theory c. 1986, anticipating much of the progress of the decades to follow.
| 1986-04-25
| 2015-06-26
|
[
"physics.pop-ph",
"hep-th"
] |
Paul Ginsparg and Sheldon Glashow
|
hep-th/9108028
|
Applied Conformal Field Theory
|
These lectures consisted of an elementary introduction to conformal field
theory, with some applications to statistical mechanical systems, and fewer to
string theory.
Contents:
1. Conformal theories in d dimensions
2. Conformal theories in 2 dimensions
3. The central charge and the Virasoro algebra
4. Kac determinant and unitarity
5. Identication of m = 3 with the critical Ising model
6. Free bosons and fermions
7. Free fermions on a torus
8. Free bosons on a torus
9. Affine Kac-Moody algebras and coset constructions
10. Advanced applications
| 1988-11-11
| 2008-02-06
|
[
"hep-th"
] |
Paul Ginsparg
|
math/9201207
|
The Rademacher cotype of operators from $l_\infty^N$
|
We show that for any operator $T:l_\infty^N\to Y$, where $Y$ is a Banach
space, that its cotype 2 constant, $K_2(T)$, is related to its $(2,1)$-summing
norm, $\pi_{2,1}(T)$, by $K_2(T) \le c \log\log N \pi_{2,1}(T) $. Thus, we can
show that there is an operator $T:C(K)\to Y$ that has cotype 2, but is not
2-summing.
| 1989-11-17
| 2008-02-03
|
[
"math.FA"
] |
Stephen J. Montgomery-Smith and Michel Talagrand
|
math/9201206
|
On the volume of the intersection of two $L_p^n$ balls
|
This note deals with the following problem, the case $p=1$, $q=2$ of which
was introduced to us by Vitali Milman: What is the volume left in the $L_p^n$
ball after removing a t-multiple of the $L_q^n$ ball? Recall that the $L_r^n$
ball is the set $\{(t_1,t_2,\dots,t_n);\ t_i\in{\bf R},\
n^{-1}\sum_{i=1}^n|t_i|^r\le 1\}$ and note that for $0<p<q<\infty$ the $L_q^n$
ball is contained in the $L_p^n$ ball.
In Corollary 4 we show that, after normalizing Lebesgue measure so that the
volume of the $L_p^n$ ball is one, the answer to the problem above is of order
$e^{-ct^pn^{p/q}}$ for $T<t<{1\over 2}n^ {{1\over p}-{1\over q}}$, where $c$
and $T$ depend on $p$ and $q$ but not on $n$.
The main theorem, Theorem 3, deals with the corresponding question for the
surface measure of the $L_p^n$ sphere.
| 1989-11-09
| 2008-02-03
|
[
"math.FA",
"math.MG"
] |
Gideon Schechtman and Joel Zinn
|
math/9201239
|
A note on canonical functions
|
We construct a generic extension in which the aleph_2 nd canonical function
on aleph_1 exists.
| 1989-04-15
| 2009-09-25
|
[
"math.LO"
] |
Thomas Jech, Saharon Shelah
|
math/9201205
|
Volume ratios and a reverse isoperimetric inequality
|
It is shown that if $C$ is an $n$-dimensional convex body then there is an
affine image $\widetilde C$ of $C$ for which
$${|\partial \widetilde C|\over |\widetilde C|^{n-1\over n}}$$
is no larger than the corresponding expression for a regular $n$-dimensional
``tetrahedron''. It is also shown that among $n$-dimensional subspaces of $L_p$
(for each $p\in [1,\infty]), \ell^n_p$ has maximal volume ratio.\vskip3in
| 1989-10-26
| 2008-02-03
|
[
"math.MG",
"math.FA"
] |
Keith Ball
|
math/9201204
|
Shadows of convex bodies
|
It is proved that if $C$ is a convex body in ${\Bbb R}^n$ then $C$ has an
affine image $\widetilde C$ (of non-zero volume) so that if $P$ is any
1-codimensional orthogonal projection,
$$|P\widetilde C| \ge |\widetilde C|^{n-1\over n}.$$
It is also shown that there is a pathological body, $K$, all of whose
orthogonal projections have volume about $\sqrt{n}$ times as large as
$|K|^{n-1\over n}$.
| 1989-10-26
| 2016-09-06
|
[
"math.MG",
"math.FA"
] |
Keith Ball
|
math/9201203
|
Convex bodies with few faces
|
It is proved that if $u_1,\ldots, u_n$ are vectors in ${\Bbb R}^k, k\le n, 1
\le p < \infty$ and
$$r = ({1\over k} \sum ^n_1 |u_i|^p)^{1\over p}$$
then the volume of the symmetric convex body whose boundary functionals are
$\pm u_1,\ldots, \pm u_n$, is bounded from below as
$$|\{ x\in {\Bbb R}^k\colon \ |\langle x,u_i\rangle | \le 1 \ \hbox{for
every} \ i\}|^{1\over k} \ge {1\over \sqrt{\rho}r}.$$
An application to number theory is stated.
| 1989-10-26
| 2016-09-06
|
[
"math.MG",
"math.FA"
] |
Keith Ball (Texas A&M University) and Alain Pajor (Paris VII)
|
cs/9301111
|
Nested satisfiability
|
A special case of the satisfiability problem, in which the clauses have a
hierarchical structure, is shown to be solvable in linear time, assuming that
the clauses have been represented in a convenient way.
| 1990-01-01
| 2008-02-03
|
[
"cs.CC"
] |
Donald E. Knuth
|
cs/9301112
|
A note on digitized angles
|
We study the configurations of pixels that occur when two digitized straight
lines meet each other.
| 1990-04-01
| 2008-02-03
|
[
"cs.GR"
] |
Donald E. Knuth
|
math/9201303
|
Stable husbands
|
Suppose $n$ boys and $n$ girls rank each other at random. We show that any
particular girl has at least $({1\over 2}-\epsilon) \ln n$ and at most
$(1+\epsilon)\ln n$ different husbands in the set of all Gale/Shapley stable
matchings defined by these rankings, with probability approaching 1 as $n \to
\infty$, if $\epsilon$ is any positive constant. The proof emphasizes general
methods that appear to be useful for the analysis of many other combinatorial
algorithms.
| 1990-01-01
| 2008-02-03
|
[
"math.CO",
"math.PR"
] |
Donald E. Knuth, Rajeev Motwani, and Boris Pittel
|
math/9201276
|
New examples of manifolds with completely integrable geodesic flows
|
We construct Riemannian manifolds with completely integrable geodesic flows,
in particular various nonhomogeneous examples. The methods employed are a
modification of Thimm's method, Riemannian submersions and connected sums.
| 1990-12-04
| 2008-02-03
|
[
"math.DS",
"math.DG"
] |
Gabriel Paternain, Ralf J. Spatzier
|
math/9201275
|
The Julia sets and complex singularities in hierarchical Ising models
|
We study the analytical continuation in the complex plane of free energy of
the Ising model on diamond-like hierarchical lattices. It is known that the
singularities of free energy of this model lie on the Julia set of some
rational endomorphism $f$ related to the action of the Migdal-Kadanoff
renorm-group. We study the asymptotics of free energy when temperature goes
along hyperbolic geodesics to the boundary of an attractive basin of $f$. We
prove that for almost all (with respect to the harmonic measure) geodesics the
complex critical exponent is common, and compute it.
| 1990-09-26
| 2009-10-22
|
[
"math.DS",
"math-ph",
"math.MP"
] |
Pavel Bleher, Mikhail Lyubich
|
math/9201274
|
One-dimensional maps and Poincar\'e metric
|
Invertible compositions of one-dimensional maps are studied which are assumed
to include maps with non-positive Schwarzian derivative and others whose sum of
distortions is bounded. If the assumptions of the Koebe principle hold, we show
that the joint distortion of the composition is bounded. On the other hand, if
all maps with possibly non-negative Schwarzian derivative are almost
linear-fractional and their nonlinearities tend to cancel leaving only a small
total, then they can all be replaced with affine maps with the same domains and
images and the resulting composition is a very good approximation of the
original one. These technical tools are then applied to prove a theorem about
critical circle maps.
| 1990-08-12
| 2016-09-06
|
[
"math.DS"
] |
Grzegorz Swiatek
|
math/9201273
|
Remarks on iterated cubic maps
|
This note will discuss the dynamics of iterated cubic maps from the real or
complex line to itself, and will describe the geography of the parameter space
for such maps. It is a rough survey with few precise statements or proofs, and
depends strongly on work by Douady, Hubbard, Branner and Rees.
| 1990-05-12
| 2008-02-03
|
[
"math.DS"
] |
John W. Milnor
|
math/9201272
|
Dynamics in one complex variable: introductory lectures
|
These notes study the dynamics of iterated holomorphic mappings from a
Riemann surface to itself, concentrating on the classical case of rational maps
of the Riemann sphere. They are based on introductory lectures given at Stony
Brook during the Fall Term of 1989-90. These lectures are intended to introduce
the reader to some key ideas in the field, and to form a basis for further
study. The reader is assumed to be familiar with the rudiments of complex
variable theory and of two-dimensional differential geometry.
| 1990-04-20
| 2016-09-06
|
[
"math.DS",
"math.CV"
] |
John W. Milnor
|
math/9201271
|
Conformal dynamics problem list
|
This is a list of unsolved problems given at the Conformal Dynamics
Conference which was held at SUNY Stony Brook in November 1989. Problems were
contributed by the editor and the other authors.
| 1990-01-18
| 2009-09-25
|
[
"math.DS"
] |
Ben Bielefeld (editor), Adrien Douady, Curt McMullen, Jack Milnor,
Misuhiro Shishikura, Folkert Tangerman, Peter Veerman
|
math/9201220
|
The proportional UAP characterizes weak Hilbert spaces
|
We prove that a Banach space has the uniform approximation property with
proportional growth of the uniformity function iff it is a weak Hilbert space.
| 1990-12-31
| 2008-02-03
|
[
"math.FA"
] |
William B. Johnson and Gilles Pisier
|
math/9201219
|
On quotients of Banach spaces having shrinking unconditional bases
|
It is proved that if a Banach space $Y$ is a quotient of a Banach space
having a shrinking unconditional basis, then every normalized weakly null
sequence in $Y$ has an unconditional subsequence. The proof yields the
corollary that every quotient of Schreier's space is $c_o$-saturated.
| 1990-11-16
| 2008-02-03
|
[
"math.FA"
] |
Edward Odell
|
math/9201216
|
Some deviation inequalities
|
We introduce a concentration property for probability measures on
$\scriptstyle{R^n}$, which we call Property~($\scriptstyle\tau$); we show that
this property has an interesting stability under products and contractions
(Lemmas 1,~2,~3). Using property~($\scriptstyle\tau$), we give a short proof
for a recent deviation inequality due to Talagrand. In a third section, we also
recover known concentration results for Gaussian measures using our approach.}
| 1990-09-05
| 2009-09-25
|
[
"math.FA"
] |
Bernard Maurey
|
math/9201215
|
p-summing operators on injective tensor products of spaces
|
Let $X,Y$ and $Z$ be Banach spaces, and let $\prod_p(Y,Z) (1\leq p<\infty)$
denote the space of $p$-summing operators from $Y$ to $Z$. We show that, if $X$
is a {\it \$}$_\infty$-space, then a bounded linear operator $T: X\hat
\otimes_\epsilon Y\longrightarrow Z$ is 1-summing if and only if a naturally
associated operator $T^#: X\longrightarrow \prod_1(Y,Z)$ is 1-summing. This
result need not be true if $X$ is not a {\it \$}$_\infty$-space. For $p>1$,
several examples are given with $X=C[0,1]$ to show that $T^#$ can be
$p$-summing without $T$ being $p$-summing. Indeed, there is an operator $T$ on
$C[0,1]\hat \otimes_\epsilon \ell_1$ whose associated operator $T^#$ is
2-summing, but for all $N\in \N$, there exists an $N$-dimensional subspace $U$
of $C[0,1]\hat \otimes_\epsilon \ell_1$ such that $T$ restricted to $U$ is
equivalent to the identity operator on $\ell^N_\infty$. Finally, we show that
there is a compact Hausdorff space $K$ and a bounded linear operator $T:\
C(K)\hat \otimes_\epsilon \ell_1\longrightarrow \ell_2$ for which $T^#:\
C(K)\longrightarrow \prod_1(\ell_1, \ell_2)$ is not 2-summing.
| 1990-07-23
| 2008-02-03
|
[
"math.FA"
] |
Stephen J. Montgomery-Smith and Paulette Saab
|
math/9201214
|
On the complemented subspaces of X_p
|
In this paper we prove some results related to the problem of isomorphically
classifying the complemented subspaces of $X_{p}$. We characterize the
complemented subspaces of $X_{p}$ which are isomorphic to $X_{p}$ by showing
that such a space must contain a canonical complemented subspace isomorphic to
$X_{p}.$ We also give some characterizations of complemented subspaces of
$X_{p}$ isomorphic to $\ell_{p}\oplus \ell_{2}.$
| 1990-07-20
| 2008-02-03
|
[
"math.FA"
] |
Dale E. Alspach
|
math/9201213
|
Permutations of the Haar system
|
General permutations acting on the Haar system are investigated. We give a
necessary and sufficient condition for permutations to induce an isomorphism on
dyadic BMO. Extensions of this characterization to Lipschitz spaces $\lip,
(0<p\leq1)$ are obtained. When specialized to permutations which act on one
level of the Haar system only, our approach leads to a short straightforward
proof of a result due to E.M.Semyonov and B.Stoeckert.
| 1990-06-25
| 2009-09-25
|
[
"math.FA"
] |
Paul F. X. M\"uller
|
math/9201212
|
Complemented subspaces of spaces obtained by interpolation
|
If Z is a quotient of a subspace of a separable Banach space X, and V is any
separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0
and A_1 are isometric to $X\oplus V$, and any intermediate space obtained using
the real or complex interpolation method contains a complemented subspace
isomorphic to Z. Thus many properties of Banach spaces, including having
non-trivial cotype, having the Radon-Nikodym property, and having the analytic
unconditional martingale difference sequence property, do not pass to
intermediate spaces.
| 1990-06-20
| 2008-02-03
|
[
"math.FA"
] |
D. J. H. Garling and Stephen J. Montgomery-Smith
|
math/9201211
|
Nuclear operators on spaces of continuous vector-valued functions
|
Let $\Omega$ be a compact Hausdorff space, let $E$ be a Banach space, and let
$C(\Omega, E)$ stand for the Banach space of all $E$-valued continuous
functions on $\Omega$ under supnorm. In this paper we study when nuclear
operators on $C(\Omega, E)$ spaces can be completely characterized in terms of
properties of their representing vector measures. We also show that if $F$ is a
Banach space and if $T:\ C(\Omega, E)\rightarrow F$ is a nuclear operator, then
$T$ induces a bounded linear operator $T^\#$ from the space $C(\Omega)$ of
scalar valued continuous functions on $\Omega$ into $\slN(E,F)$ the space of
nuclear operators from $E$ to $F$, in this case we show that $E^*$ has the
Radon-Nikodym property if and only if $T^\#$ is nuclear whenever $T$ is
nuclear.
| 1990-03-27
| 2008-02-03
|
[
"math.FA"
] |
Paulette Saab and Brenda Smith
|
math/9201210
|
Integral Operators on Spaces of Continuous Vector-valued Functions
|
Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let
$C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$
under the uniform norm. In this paper we characterize Integral operators (in
the sense of Grothendieck) on $C(X,E)$ spaces in term of their representing
vector measures. This is then used to give some applications to Nuclear
operators on $C(X,E)$ spaces.
| 1990-03-15
| 2009-09-25
|
[
"math.FA"
] |
Paulette Saab
|
math/9201209
|
Operators which factor through Banach lattices not containing c_0
|
In this supplement to [GJ1], [GJ3], we give an intrinsic characterization of
(bounded, linear) operators on Banach lattices which factor through Banach
lattices not containing a copy of $c_0$ which complements the characterization
of [GJ1], [GJ3] that an operator admits such a factorization if and only if it
can be written as the product of two operators neither of which preserves a
copy of $c_0$. The intrinsic characterization is that the restriction of the
second adjoint of the operator to the ideal generated by the lattice in its
bidual does not preserve a copy of $c_0$. This property of an operator was
introduced by C. Niculescu [N2] under the name ``strong type B".
| 1990-02-19
| 2016-09-06
|
[
"math.FA"
] |
Nassif Ghoussoub and William B. Johnson
|
math/9201240
|
Categoricity over P for first order T or categoricity for phi in
L_{omega_1 omega} can stop at aleph_k while holding for aleph_0, ...,
aleph_{k-1}
|
Suppose L is a relational language and P in L is a unary predicate. If M is
an L-structure then P(M) is the L-structure formed as the substructure of M
with domain {a: M models P(a)}. Now suppose T is a complete first order theory
in L with infinite models. Following Hodges, we say that T is relatively
lambda-categorical if whenever M, N models T, P(M)=P(N), |P(M)|= lambda then
there is an isomorphism i:M-> N which is the identity on P(M). T is relatively
categorical if it is relatively lambda-categorical for every lambda. The
question arises whether the relative lambda-categoricity of T for some lambda
>|T| implies that T is relatively categorical.
In this paper, we provide an example, for every k>0, of a theory T_k and an
L_{omega_1 omega} sentence varphi_k so that T_k is relatively
aleph_n-categorical for n < k and varphi_k is aleph_n-categorical for n<k but
T_k is not relatively beth_k-categorical and varphi_k is not
beth_k-categorical.
| 1990-01-15
| 2008-02-03
|
[
"math.LO"
] |
Bradd Hart, Saharon Shelah
|
math/9201241
|
The primal framework. I
|
This the first of a series of articles dealing with abstract classification
theory. The apparatus to assign systems of cardinal invariants to models of a
first order theory (or determine its impossibility) is developed in [Sh:a]. It
is natural to try to extend this theory to classes of models which are
described in other ways. Work on the classification theory for nonelementary
classes [Sh:88] and for universal classes [Sh:300] led to the conclusion that
an axiomatic approach provided the best setting for developing a theory of
wider application. In the first chapter we describe the axioms on which the
remainder of the article depends and give some examples and context to justify
this level of generality. The study of universal classes takes as a primitive
the notion of closing a subset under functions to obtain a model. We replace
that concept by the notion of a prime model. We begin the detailed discussion
of this idea in Chapter II. One of the important contributions of
classification theory is the recognition that large models can often be
analyzed by means of a family of small models indexed by a tree of height at
most omega. More precisely, the analyzed model is prime over such a tree.
Chapter III provides sufficient conditions for prime models over such trees to
exist.
| 1990-01-15
| 2009-09-25
|
[
"math.LO"
] |
John T. Baldwin, Saharon Shelah
|
math/9201242
|
Full reflection of stationary sets below aleph_omega
|
It is consistent that for every n >= 2, every stationary subset of omega_n
consisting of ordinals of cofinality omega_k where k = 0 or k <= n-3 reflects
fully in the set of ordinals of cofinality omega_{n-1}. We also show that this
result is best possible.
| 1990-01-15
| 2008-02-03
|
[
"math.LO"
] |
Thomas Jech, Saharon Shelah
|
math/9201218
|
The plank problem for symmetric bodies
|
Given a symmetric convex body $C$ and $n$ hyperplanes in an Euclidean space,
there is a translate of a multiple of $C$, at least ${1\over n+1}$ times as
large, inside $C$, whose interior does not meet any of the hyperplanes. The
result generalizes Bang's solution of the plank problem of Tarski and has
applications to Diophantine approximation.
| 1990-09-25
| 2009-10-22
|
[
"math.MG",
"math.FA"
] |
Keith Ball
|
math/9201217
|
Ellipsoids of maximal volume in convex bodies
|
The largest discs contained in a regular tetrahedron lie in its faces. The
proof is closely related to the theorem of Fritz John characterising ellipsoids
of maximal volume contained in convex bodies.
| 1990-09-25
| 2009-09-25
|
[
"math.MG",
"math.FA"
] |
Keith Ball
|
math/9201208
|
Remarks on Talagrand's deviation inequality for Rademacher functions
|
Recently Talagrand [T] estimated the deviation of a function on $\{0,1\}^n$
from its median in terms of the Lipschitz constant of a convex extension of $f$
to $\ell ^n_2$; namely, he proved that
$$P(|f-M_f| > c) \le 4 e^{-t^2/4\sigma ^2}$$ where $\sigma$ is the Lipschitz
constant of the extension of $f$ and $P$ is the natural probability on
$\{0,1\}^n$.
Here we extend this inequality to more general product probability spaces; in
particular, we prove the same inequality for $\{0,1\}^n$ with the product
measure $((1-\eta)\delta _0 + \eta \delta _1)^n$. We believe this should be
useful in proofs involving random selections. As an illustration of possible
applications we give a simple proof (though not with the right dependence on
$\varepsilon$) of the Bourgain, Lindenstrauss, Milman result [BLM] that for
$1\le r < s \le 2$ and $\varepsilon >0$, every $n$-dimensional subspace of $L_s
\ (1+\varepsilon)$-embeds into $\ell ^N_r$ with $N = c(r,s,\varepsilon)n$.
| 1990-02-16
| 2016-09-06
|
[
"math.PR",
"math.FA"
] |
William B. Johnson and Gideon Schechtman
|
math/9201301
|
Involutory Hopf algebras and 3-manifold invariants
|
We establish a 3-manifold invariant for each finite-dimensional, involutory
Hopf algebra. If the Hopf algebra is the group algebra of a group $G$, the
invariant counts homomorphisms from the fundamental group of the manifold to
$G$. The invariant can be viewed as a state model on a Heegaard diagram or a
triangulation of the manifold. The computation of the invariant involves tensor
products and contractions of the structure tensors of the algebra. We show that
every formal expression involving these tensors corresponds to a unique
3-manifold modulo a well-understood equivalence. This raises the possibility of
an algorithm which can determine whether two given 3-manifolds are
homeomorphic.
| 1990-05-19
| 2016-09-06
|
[
"math.QA",
"math.GT"
] |
Greg Kuperberg (UC Berkeley)
|
cs/9301113
|
Textbook examples of recursion
|
We discuss properties of recursive schemas related to McCarthy's ``91
function'' and to Takeuchi's triple recursion. Several theorems are proposed as
interesting candidates for machine verification, and some intriguing open
questions are raised.
| 1991-08-01
| 2008-02-03
|
[
"cs.CC"
] |
Donald E. Knuth
|
cs/9301115
|
Context-free multilanguages
|
This article is a sketch of ideas that were once intended to appear in the
author's famous series, "The Art of Computer Programming". He generalizes the
notion of a context-free language from a set to a multiset of words over an
alphabet. The idea is to keep track of the number of ways to parse a string.
For example, "fruit flies like a banana" can famously be parsed in two ways;
analogous examples in the setting of programming languages may yet be important
in the future.
The treatment is informal but essentially rigorous.
| 1991-12-01
| 2008-02-03
|
[
"cs.DS"
] |
Donald E. Knuth
|
cs/9301114
|
Theory and practice
|
The author argues to Silicon Valley that the most important and powerful part
of computer science is work that is simultaneously theoretical and practical.
He particularly considers the intersection of the theory of algorithms and
practical software development. He combines examples from the development of
the TeX typesetting system with clever jokes, criticisms, and encouragements.
| 1991-11-01
| 2008-02-03
|
[
"cs.GL"
] |
Donald E. Knuth
|
hep-th/9112076
|
Lectures on W algebras and W gravity
|
We give a review of the extended conformal algebras, known as $W$ algebras,
which contain currents of spins higher than 2 in addition to the
energy-momentum tensor. These include the non-linear $W_N$ algebras; the linear
$W_\infty$ and $W_{1+\infty}$ algebras; and their super-extensions. We discuss
their applications to the construction of $W$-gravity and $W$-string theories.
| 1991-12-31
| 2007-05-23
|
[
"hep-th"
] |
C.N. Pope
|
hep-th/9201001
|
Combinatorics of the Modular Group II: the Kontsevich integrals
|
We study algebraic aspects of Kontsevich integrals as generating functions
for intersection theory over moduli space and review the derivation of Virasoro
and KdV constraints.
1. Intersection numbers
2. The Kontsevich integral
2.1. The main theorem
2.2 Expansion of Z on characters and Schur functions
2.3 Proof of the first part of the Theorem
3. From Grassmannians to KdV
4. Matrix Airy equation and Virasoro highest weight conditions
5. Genus expansion
6. Singular behaviour and Painlev'e equation.
7. Generalization to higher degree potentials
| 1991-12-31
| 2016-09-06
|
[
"hep-th",
"math.QA"
] |
C. Itzykson and J.-B. Zuber
|
hep-th/9112074
|
Non-linear WKB Analysis of the String Equation
|
We apply non-linear WKB analysis to the study of the string equation. Even
though the solutions obtained with this method are not exact, they approximate
extremely well the true solutions, as we explicitly show using numerical
simulations. ``Physical'' solutions are seen to be separatrices corresponding
to degenerate Riemann surfaces. We obtain an analytic approximation in
excellent agreement with the numerical solution found by Parisi et al. for the
$k=3$ case.
| 1991-12-30
| 2010-11-01
|
[
"hep-th"
] |
F. Fucito, A. Gamba, M. Martellini and O. Ragnisco
|
hep-th/9112075
|
Exactly Solvable Potentials and Quantum Algebras
|
A set of exactly solvable one-dimensional quantum mechanical potentials is
described. It is defined by a finite-difference-differential equation
generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller
potentials. General solution includes Shabat's infinite number soliton system
and leads to raising and lowering operators satisfying $q$-deformed harmonic
oscillator algebra. In the latter case energy spectrum is purely exponential
and physical states form a reducible representation of the quantum conformal
algebra $su_q(1,1)$.
| 1991-12-30
| 2009-01-23
|
[
"hep-th"
] |
V.Spiridonov
|
hep-th/9112073
|
Higher-Rank Supersymmetry and Topological Field Theory
|
The $N=2$ minimal superconformal model can be twisted yielding an example of
topological conformal field theory. In this article we investigate a Lie
theoretic extension of this process.
| 1991-12-25
| 2015-06-26
|
[
"hep-th"
] |
Toshiya Kawai, Taku Uchino and Sun-Kil Yang
|
hep-th/9112071
|
Three Manifolds and Graph Invariants
|
We show how the Turaev--Viro invariant can be understood within the framework
of Chern--Simons theory with gauge group SU(2). We also describe a new
invariant for certain class of graphs by interpreting the triangulation of a
manifold as a graph consisiting of crossings and vertices with three lines. We
further show, for $S^3$ and $RP^3$, that the Turaev-Viro invariant is the
square of the absolute value of their respective partition functions in SU(2)
Chern--Simons theory and give a method of evaluating the later in a closed form
for lens spaces $L_{p,1}$.
| 1991-12-24
| 2008-02-03
|
[
"hep-th",
"math.QA"
] |
S. Kalyana Rama and Siddhartha Sen
|
hep-th/9112072
|
Partition Functions and Topology-Changing Amplitudes in the 3D Lattice
Gravity of Ponzano and Regge
|
We define a physical Hilbert space for the three-dimensional lattice gravity
of Ponzano and Regge and establish its isomorphism to the ones in the $ISO(3)$
Chern-Simons theory. It is shown that, for a handlebody of any genus, a
Hartle-Hawking-type wave-function of the lattice gravity transforms into the
corresponding state in the Chern-Simons theory under this isomorphism. Using
the Heegaard splitting of a three-dimensional manifold, a partition function of
each of these theories is expressed as an inner product of such wave-functions.
Since the isomorphism preserves the inner products, the partition function of
the two theories are the same for any closed orientable manifold. We also
discuss on a class of topology-changing amplitudes in the lattice gravity and
their relation to the ones in the Chern-Simons theory.
| 1991-12-24
| 2009-09-17
|
[
"hep-th"
] |
Hirosi Ooguri
|
hep-th/9112070
|
Generalized Duality in Curved String-Backgrounds
|
The elements of $O(d,d,\Z)$ are shown to be discrete symmetries of the space
of curved string backgrounds that are independent of $d$ coordinates. The
explicit action of the symmetries on the backgrounds is described. Particular
attention is paid to the dilaton transformation. Such symmetries identify
different cosmological solutions and other (possibly) singular backgrounds; for
example, it is shown that a compact black string is dual to a charged black
hole. The extension to the heterotic string is discussed.
| 1991-12-23
| 2009-10-22
|
[
"hep-th"
] |
Amit Giveon and Martin Rocek
|
hep-th/9112069
|
Unitary And Hermitian Matrices In An External Field II: The Kontsevich
Model And Continuum Virasoro Constraints
|
We give a simple derivation of the Virasoro constraints in the Kontsevich
model, first derived by Witten. We generalize the method to a model of unitary
matrices, for which we find a new set of Virasoro constraints. Finally we
discuss the solution for symmetric matrices in an external field.
| 1991-12-23
| 2009-10-22
|
[
"hep-th"
] |
David J. Gross and Michael J. Newman
|
hep-th/9112068
|
On the General Structure of Hamiltonian Reductions of the Wznw Theory
|
The structure of Hamiltonian reductions of the Wess-Zumino-Novikov-Witten
(WZNW) theory by first class Kac-Moody constraints is analyzed in detail. Lie
algebraic conditions are given for ensuring the presence of exact
integrability, conformal invariance and $\cal W$-symmetry in the reduced
theories. A Lagrangean, gauged WZNW implementation of the reduction is
established in the general case and thereby the path integral as well as the
BRST formalism are set up for studying the quantum version of the reduction.
The general results are applied to a number of examples. In particular, a
${\cal W}$-algebra is associated to each embedding of $sl(2)$ into the simple
Lie algebras by using purely first class constraints. The importance of these
$sl(2)$ systems is demonstrated by showing that they underlie the
$W_n^l$-algebras as well. New generalized Toda theories are found whose chiral
algebras are the ${\cal W}$-algebras belonging to the half-integral $sl(2)$
embeddings, and the ${\cal W}$-symmetry of the effective action of those
generalized Toda theories associated with the integral gradings is exhibited
explicitly.
| 1991-12-22
| 2007-05-23
|
[
"hep-th"
] |
L. Feher, L. O'raifeartaigh, P. Ruelle, I. Tsutsui and A. Wipf
|
hep-th/9112066
|
The Solution Space of the Unitary Matrix Model String Equation and the
Sato Grassmannian
|
The space of all solutions to the string equation of the symmetric unitary
one-matrix model is determined. It is shown that the string equation is
equivalent to simple conditions on points $V_1$ and $V_2$ in the big cell $\Gr$
of the Sato Grassmannian $Gr$. This is a consequence of a well-defined
continuum limit in which the string equation has the simple form $\lb \cp
,\cq_- \rb =\hbox{\rm 1}$, with $\cp$ and $\cq_-$ $2\times 2$ matrices of
differential operators. These conditions on $V_1$ and $V_2$ yield a simple
system of first order differential equations whose analysis determines the
space of all solutions to the string equation. This geometric formulation leads
directly to the Virasoro constraints $\L_n\,(n\geq 0)$, where $\L_n$ annihilate
the two modified-KdV $\t$-functions whose product gives the partition function
of the Unitary Matrix Model.
| 1991-12-21
| 2009-10-22
|
[
"hep-th"
] |
Konstantinos N. Anagnostopoulos, Mark J. Bowick and Albert Schwarz
|
hep-th/9112062
|
Quantum Mechanics and Black Holes in Four-Dimensional String Theory
|
In previous papers we have shown how strings in a two-dimensional target
space reconcile quantum mechanics with general relativity, thanks to an
infinite set of conserved quantum numbers, ``W-hair'', associated with
topological soliton-like states. In this paper we extend these arguments to
four dimensions, by considering explicitly the case of string black holes with
radial symmetry. The key infinite-dimensional W-symmetry is associated with the
$\frac{SU(1,1)}{U(1)}$ coset structure of the dilaton-graviton sector that is a
model-independent feature of spherically symmetric four-dimensional strings.
Arguments are also given that the enormous number of string {\it discrete
(topological)} states account for the maintenance of quantum coherence during
the (non-thermal) stringy evaporation process, as well as quenching the large
Hawking-Bekenstein entropy associated with the black hole. Defining the latter
as the measure of the loss of information for an observer at infinity, who -
ignoring the higher string quantum numbers - keeps track only of the classical
mass,angular momentum and charge of the black hole, one recovers the familiar a
quadratic dependence on the black-hole mass by simple counting arguments on the
asymptotic density of string states in a linear-dilaton background.
| 1991-12-20
| 2009-09-11
|
[
"hep-th"
] |
J. Ellis, N. Mavromatos, and D. Nanopoulos
|
hep-th/9112060
|
W Gravity From Chern--Simons Theory
|
Starting with three dimensional Chern--Simons theory with gauge group
$Sl(N,R)$, we derive an action $S_{cov}$ invariant under both left and right
$W_N$ transformations. We give an interpretation of $S_{cov}$ in terms of
anomalies, and discuss its relation with Toda theory.
| 1991-12-20
| 2009-10-22
|
[
"hep-th"
] |
Jan de Boer and Jacob Goeree
|
hep-th/9112063
|
Integrability of the quantum KdV equation at c = -2
|
We present a simple a direct proof of the complete integrability of the
quantum KdV equation at $c=-2$, with an explicit description of all the
conservation laws.
| 1991-12-20
| 2009-10-22
|
[
"hep-th"
] |
P. Di Francesco, P. Mathieu and D. Senechal
|
hep-th/9112061
|
Symmetries and Special States in Two Dimensional String Theory
|
We use the W-infinity symmetry of c=1 quantum gravity to compute matrix model
special state correlation functions. The results are compared, and found to
agree, with expectations from the Liouville model.
| 1991-12-20
| 2009-10-22
|
[
"hep-th"
] |
Ulf H. Danielsson
|
hep-th/9112065
|
Euclidean Black Hole Vortices
|
We argue the existence of solutions of the Euclidean Einstein equations that
correspond to a vortex sitting at the horizon of a black hole. We find the
asymptotic behaviours, at the horizon and at infinity, of vortex solutions for
the gauge and scalar fields in an abelian Higgs model on a Euclidean
Schwarzschild background and interpolate between them by integrating the
equations numerically. Calculating the backreaction shows that the effect of
the vortex is to cut a slice out of the Euclidean Schwarzschild geometry.
Consequences of these solutions for black hole thermodynamics are discussed.
| 1991-12-20
| 2011-04-20
|
[
"hep-th"
] |
Fay Dowker, Ruth Gregory and Jennie Traschen
|
hep-th/9112064
|
Topological gauge theories from supersymmetric quantum mechanics on
spaces of connections
|
We rederive the recently introduced $N=2$ topological gauge theories,
representing the Euler characteristic of moduli spaces ${\cal M}$ of
connections, from supersymmetric quantum mechanics on the infinite dimensional
spaces ${\cal A}/{\cal G}$ of gauge orbits. To that end we discuss variants of
ordinary supersymmetric quantum mechanics which have meaningful extensions to
infinite-dimensional target spaces and introduce supersymmetric quantum
mechanics actions modelling the Riemannian geometry of submersions and
embeddings, relevant to the projections ${\cal A}\rightarrow {\cal A}/{\cal G}$
and inclusions ${\cal M}\subset{\cal A}/{\cal G}$ respectively. We explain the
relation between Donaldson theory and the gauge theory of flat connections in
$3d$ and illustrate the general construction by other $2d$ and $4d$ examples.
| 1991-12-20
| 2015-06-26
|
[
"hep-th"
] |
M Blau and G Thompson
|
hep-th/9112050
|
Topics in String Unification
|
I discuss several aspects of strings as unified theories. After recalling the
difficulties of the simplest supersymmetric grand unification schemes I
emphasize the distinct features of string unification. An important role in
constraining the effective low energy physics from strings is played by
$duality$ symmetries. The discussed topics include the unification of coupling
constants (computation of $\sin ^2\theta _W$ and $\alpha _s$ at the weak
scale), supersymmetry breaking through gaugino condensation, and properties of
the induced SUSY-breaking soft terms. I remark that departures from
universality in the soft terms are (in contrast to the minimal SUSY model)
generically expected.
| 1991-12-19
| 2008-02-06
|
[
"hep-th"
] |
Luis E. Ibanez
|
hep-th/9112067
|
On the Symmetries of Integrability
|
We show that the Yang-Baxter equations for two dimensional models admit as a
group of symmetry the infinite discrete group $A_2^{(1)}$. The existence of
this symmetry explains the presence of a spectral parameter in the solutions of
the equations. We show that similarly, for three-dimensional vertex models and
the associated tetrahedron equations, there also exists an infinite discrete
group of symmetry. Although generalizing naturally the previous one, it is a
much bigger hyperbolic Coxeter group. We indicate how this symmetry can help to
resolve the Yang-Baxter equations and their higher-dimensional generalizations
and initiate the study of three-dimensional vertex models. These symmetries are
naturally represented as birational projective transformations. They may
preserve non trivial algebraic varieties, and lead to proper parametrizations
of the models, be they integrable or not. We mention the relation existing
between spin models and the Bose-Messner algebras of algebraic combinatorics.
Our results also yield the generalization of the condition $q^n=1$ so often
mentioned in the theory of quantum groups, when no $q$ parameter is available.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
M. Bellon, J-M. Maillard, C. Viallet
|
hep-th/9112057
|
One-Point Functions of Loops and Constraints Equations of the
Multi-Matrix Models at finite N
|
We derive one-point functions of the loop operators of Hermitian matrix-chain
models at finite $N$ in terms of differential operators acting on the partition
functions. The differential operators are completely determined by recursion
relations from the Schwinger-Dyson equations. Interesting observation is that
these generating operators of the one-point functions satisfy
$W_{1+\infty}$-like algebra. Also, we obtain constraint equations on the
partition functions in terms of the differential operators. These constraint
equations on the partition functions define the symmetries of the matrix models
at off-critical point before taking the double scaling limit.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
Changrim Ahn and Kazuyasu Shigemoto
|
hep-th/9112049
|
Flat Holomorphic Connections and Picard-Fuchs Identities From $N=2$
Supergravity
|
We show that in special K\"ahler geometry of $N=2$ space-time supergravity
the gauge variant part of the connection is holomorphic and flat (in a
Riemannian sense). A set of differential identities (Picard-Fuchs identities)
are satisfied on a holomorphic bundle. The relationship with the differential
equations obeyed by the periods of the holomorphic three form of Calabi-Yau
manifolds is outlined.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
Sergio Ferrara and Jan Louis
|
hep-th/9112052
|
$W$-Infinity Ward Identities and Correlation Functions in the $C=1$
Matrix Model
|
We explore consequences of $W$-infinity symmetry in the fermionic field
theory of the $c=1$ matrix model. We derive exact Ward identities relating
correlation functions of the bilocal operator. These identities can be
expressed as equations satisfied by the effective action of a {\it three}
dimensional theory and contain non-perturbative information about the model. We
use these identities to calculate the two point function of the bilocal
operator in the double scaling limit. We extract the operator whose two point
correlator has a {\it single} pole at an (imaginary) integer value of the
energy. We then rewrite the \winf~ charges in terms of operators in the matrix
model and use this derive constraints satisfied by the partition function of
the matrix model with a general time dependent potential.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
Sumit R. Das, Avinash Dhar, Gautam Mandal and Spenta R. Wadia
|
hep-th/9112053
|
C.S.Xiong
|
We generalize Toda--like integrable lattice systems to non--symmetric case.
We show that they possess the bi--Hamiltonian structure.
| 1991-12-19
| 2015-06-26
|
[
"hep-th"
] |
Generalized Integrable Lattice Systems
|
hep-th/9112056
|
Mirror Manifolds And Topological Field Theory
|
These notes are devoted to explaining aspects of the mirror manifold problem
that can be naturally understood from the point of view of topological field
theory. Basically this involves studying the topological field theories made by
twisting $N=2$ sigma models. This is mainly a review of old results, except for
the discussion in \S7 of certain facts that may be relevant to constructing the
``mirror map'' between mirror moduli spaces.
| 1991-12-19
| 2007-05-23
|
[
"hep-th"
] |
Edward Witten
|
hep-th/9112058
|
Loop Equations and Virasoro Constraints in Matrix Models
|
In the first part of the talk, I review the applications of loop equations to
the matrix models and to 2-dimensional quantum gravity which is defined as
their continuum limit. The results concerning multi-loop correlators for low
genera and the Virasoro invariance are discussed. The second part is devoted to
the Kontsevich matrix model which is equivalent to 2-dimensional topological
gravity. I review the Schwinger--Dyson equations for the Kontsevich model as
well as their explicit solution in genus zero. The relation between the
Kontsevich model and the continuum limit of the hermitean one-matrix model is
discussed.
| 1991-12-19
| 2007-05-23
|
[
"hep-th"
] |
Yu.Makeenko
|
hep-th/9112051
|
Topological Matter in Two Dimensions
|
Topological quantum field theories containing matter fields are constructed
by twisting $N=2$ supersymmetric quantum field theories. It is shown that $N=2$
chiral (antichiral) multiplets lead to topological sigma models while $N=2$
twisted chiral (twisted antichiral) multiplets lead to Landau-Ginzburg type
topological quantum field theories. In addition, topological gravity in two
dimensions is formulated using a gauge principle applied to the topological
algebra which results after the twisting of $N=2$ supersymmetry.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
J.M.F. Labastida and P.M. Llatas
|
hep-th/9112054
|
Internal Frame Dragging and a Global Analog of the Aharonov-Bohm Effect
|
It is shown that the breakdown of a {\it global} symmetry group to a discrete
subgroup can lead to analogues of the Aharonov-Bohm effect. At sufficiently low
momentum, the cross-section for scattering of a particle with nontrivial $\Z_2$
charge off a global vortex is almost equal to (but definitely different from)
maximal Aharonov-Bohm scattering; the effect goes away at large momentum. The
scattering of a spin-1/2 particle off a magnetic vortex provides an amusing
experimentally realizable example.
| 1991-12-19
| 2009-10-22
|
[
"hep-th"
] |
John March-Russell, John Preskill, and Frank Wilczek
|
hep-th/9112048
|
$O(N)$ Vector Field Theories in the Double Scaling Limit
|
$O(N)$ invariant vector models have been shown to possess non-trivial scaling
large $N$ limits, at least perturbatively within the loop expansion, a property
they share with matrix models of 2D quantum gravity. In contrast with matrix
models, however, vector models can be solved in arbitrary dimensions. We
present here the analysis of field theory vector models in $d$ dimensions and
discuss the nature and form of the critical behaviour. The double scaling limit
corresponds for $d>1$ to a situation where a bound state of the $N$-component
fundamental vector field $\phi$, associated with the $\phi^2$ composite
operator, becomes massless, while the field $\phi$ itself remains massive. The
limiting model can be described by an effective local interaction for the
corresponding $O(N)$ invariant field. It has a physical interpretation as
describing the statistical properties of a class of branched polymers.\par It
is hoped that the $O(N)$ vector models, which can be investigated in their most
general form, can serve as a test ground for new ideas about the behaviour of
2D quantum gravity coupled with $d>1$ matter.
| 1991-12-19
| 2011-04-20
|
[
"hep-th"
] |
J. Zinn-Justin
|
hep-th/9112055
|
A Conformal Field Theory Formalism from Integrable Hierarchies via the
Kontsevich--Miwa Transform
|
We attempt a direct derivation of a conformal field theory description of 2D
quantum gravity~+~matter from the formalism of integrable hierarchies subjected
to Virasoro constraints. The construction is based on a generalization of the
Kontsevich parametrization of the KP times by introducing Miwa parameters into
it. The resulting Kontsevich--Miwa transform can be applied to the Virasoro
constraints provided the Miwa parameters are related to the background charge
$Q$ of the Virasoro generators on the hierarchy. We then recover the field
content of the David-Distler-Kawai formalism, with the matter theory
represented by a scalar with the background charge $Q_m=Q-{Q\over 2}$. In
particular, the tau function is related to the correlator of a product of the
`21' operators of the minimal model with central charge $d=1-3Q_m^2$.
| 1991-12-19
| 2010-12-01
|
[
"hep-th"
] |
A.M.Semikhatov
|
hep-th/9112047
|
Abelian Landau--Ginzburg Orbifolds and Mirror Symmetry
|
We construct a class of Heterotic String vacua described by Landau--Ginzburg
theories and consider orbifolds of these models with respect to abelian
symmetries. For LG--vacua described by potentials in which at most three
scaling fields are coupled we explicitly construct the chiral ring and discuss
its diagonalization with respect to its most general abelian symmetry. For
theories with couplings between at most two fields we present results of an
explicit construction of the LG--potentials and their orbifolds. The emerging
space of (2,2)--theories shows a remarkable mirror symmetry. It also contains a
number of new three--generation models.
| 1991-12-18
| 2009-10-22
|
[
"hep-th"
] |
M. Kreuzer, R. Schimmrigk, H. Skarke
|
hep-th/9112046
|
SDiff(2) KP hierarchy
|
An analogue of the KP hierarchy, the SDiff(2) KP hierarchy, related to the
group of area-preserving diffeomorphisms on a cylinder is proposed. An improved
Lax formalism of the KP hierarchy is shown to give a prototype of this new
hierarchy. Two important potentials, $S$ and $\tau$, are introduced. The latter
is a counterpart of the tau function of the ordinary KP hierarchy. A
Riemann-Hilbert problem relative to the group of area-diffeomorphisms gives a
twistor theoretical description (nonlinear graviton construction) of general
solutions. A special family of solutions related to topological minimal models
are identified in the framework of the Riemann-Hilbert problem. Further,
infinitesimal symmetries of the hierarchy are constructed. At the level of the
tau function, these symmetries obey anomalous commutation relations, hence
leads to a central extension of the algebra of infinitesimal area-preserving
diffeomorphisms (or of the associated Poisson algebra).
| 1991-12-18
| 2009-10-22
|
[
"hep-th",
"nlin.SI",
"solv-int"
] |
Kanehisa Takasaki and Takashi Takebe
|
hep-th/9112043
|
Quantum Conserved Charges and S-matrices in N=2 Supersymmetric
Sine-Gordon Theory
|
We study the quantum conserved charges and S-matrices of N=2 supersymmetric
sine-Gordon theory in the framework of perturbation theory formulated in N=2
superspace. The quantum affine algebras ${\widehat {sl_{q}(2)}}$ and super
topological charges play important roles in determining the N=2 soliton
structure and S-matrices of soliton-(anti)soliton as well as soliton-breather
scattering.
| 1991-12-17
| 2008-11-26
|
[
"hep-th"
] |
Ken-ichiro Kobayashi and Tsuneo Uematsu
|
hep-th/9112039
|
Topological Approach to Alice Electrodynamics
|
We analyze the unlocalized ``Cheshire charge'' carried by ``Alice strings.''
The magnetic charge on a string loop is carefully defined, and the transfer of
magnetic charge from a monopole to a string loop is analyzed using global
topological methods. A semiclassical theory of electric charge transfer is also
described.
| 1991-12-17
| 2009-10-22
|
[
"hep-th"
] |
Martin Bucher, Hoi-Kwong Lo, and John Preskill
|
hep-th/9112038
|
Quantum Field Theory of Nonabelian Strings and Vortices
|
We develop an operator formalism for investigating the properties of
nonabelian cosmic strings (and vortices) in quantum field theory. Operators are
constructed that introduce classical string sources and that create dynamical
string loops. The operator construction in lattice gauge theory is explicitly
described, and correlation functions are computed in the strong--coupling and
weak--coupling limits. These correlation functions are used to study the
long--range interactions of nonabelian strings, taking account of
charge--screening effects due to virtual particles. Among the phenomena
investigated are the Aharonov--Bohm interactions of strings with charged
particles, holonomy interactions between string loops, string entanglement, the
transfer of ``Cheshire charge'' to a string loop, and domain wall decay via
spontaneous string nucleation. We also analyze the Aharonov--Bohm interactions
of magnetic monopoles with electric flux tubes in a confining gauge theory. We
propose that the Aharonov--Bohm effect can be invoked to distinguish among
various phases of a nonabelian gauge theory coupled to matter.
| 1991-12-17
| 2009-10-22
|
[
"hep-th"
] |
Mark Alford, Kai-Ming Lee, John March-Russell, and John Preskill
|
hep-th/9112045
|
Semiclassical Approach to Finite-N Matrix Models
|
We reformulate the zero-dimensional hermitean one-matrix model as a
(nonlocal) collective field theory, for finite~$N$. The Jacobian arising by
changing variables from matrix eigenvalues to their density distribution is
treated {\it exactly\/}. The semiclassical loop expansion turns out {\it not\/}
to coincide with the (topological) ${1\over N}$~expansion, because the
classical background has a non-trivial $N$-dependence. We derive a simple
integral equation for the classical eigenvalue density, which displays strong
non-perturbative behavior around $N\!=\!\infty$. This leads to IR singularities
in the large-$N$ expansion, but UV divergencies appear as well, despite
remarkable cancellations among the Feynman diagrams. We evaluate the free
energy at the two-loop level and discuss its regularization. A simple example
serves to illustrate the problems and admits explicit comparison with
orthogonal polynomial results.
| 1991-12-17
| 2010-11-01
|
[
"hep-th"
] |
Olaf Lechtenfeld
|
hep-th/9112041
|
Area-Preserving Diffeomorphisms and Nonlinear Integrable Systems
|
Present state of the study of nonlinear ``integrable" systems related to the
group of area-preserving diffeomorphisms on various surfaces is overviewed.
Roles of area-preserving diffeomorphisms in 4-d self-dual gravity are reviewed.
Recent progress in new members of this family, the SDiff(2) KP and Toda
hierarchies, is reported. The group of area-preserving diffeomorphisms on a
cylinder plays a key role just as the infinite matrix group GL($\infty$) does
in the ordinary KP and Toda lattice hierarchies. The notion of tau functions is
also shown to persist in these hierarchies, and gives rise to a central
extension of the corresponding Lie algebra.
| 1991-12-17
| 2008-02-03
|
[
"hep-th",
"nlin.SI",
"solv-int"
] |
Kanehisa Takasaki
|
hep-th/9112042
|
SDiff(2) Toda equation -- hierarchy, $\tau$ function, and symmetries
|
A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda
equation, is shown to have a Lax formalism and an infinite hierarchy of higher
flows. The Lax formalism is very similar to the case of the self-dual vacuum
Einstein equation and its hyper-K\"ahler version, however now based upon a
symplectic structure and the group SDiff(2) of area preserving diffeomorphisms
on a cylinder $S^1 \times \R$. An analogue of the Toda lattice tau function is
introduced. The existence of hidden SDiff(2) symmetries are derived from a
Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function
turn out to have commutator anomalies, hence give a representation of a central
extension of the SDiff(2) algebra.
| 1991-12-17
| 2009-10-22
|
[
"hep-th",
"nlin.SI",
"solv-int"
] |
Kanehisa Takasaki and Takashi Takebe
|
hep-th/9112044
|
$O(d,d)$-Covariant String Cosmology
|
The recently discovered $O(d,d)$ symmetry of the space of slowly varying
cosmological string vacua in $d+1$ dimensions is shown to be preserved in the
presence of bulk string matter. The existence of $O(d,d)$ conserved currents
allows all the equations of string cosmology to be reduced to first-order
differential equations. The perfect-fluid approximation is not
$O(d,d)$-invariant, implying that stringy fluids possess in general a
non-vanishing viscosity.
| 1991-12-17
| 2009-10-22
|
[
"hep-th"
] |
M. Gasperini and G. Veneziano
|
hep-th/9112040
|
On Detecting Discrete Cheshire Charge
|
We analyze the charges carried by loops of string in models with non-abelian
local discrete symmetry. The charge on a loop has no localized source, but can
be detected by means of the Aharonov--Bohm interaction of the loop with another
string. We describe the process of charge detection, and the transfer of charge
between point particles and string loops, in terms of gauge--invariant
correlation functions.
| 1991-12-17
| 2009-10-22
|
[
"hep-th"
] |
Martin Bucher, Kai-Ming Lee, and John Preskill
|
hep-th/9112034
|
A Novel Chiral Boson
|
We introduce a new model describing a bosonic system with chiral properties.
It consists of a free boson with two peculiar couplings to the background
geometry which generalizes the Feigen-Fuchs-Dotsenko-Fateev construction. By
choosing the two background charges of the model, it is possible to achieve any
prefixed value of the left and right central charges and, in particular, obtain
chiral bosonization. A supersymmetric version of the model is also given. We
use the latter to identify the effective action induced by chiral
superconformal matter.
| 1991-12-16
| 2009-10-22
|
[
"hep-th"
] |
Fiorenzo Bastianelli
|
hep-th/9112037
|
From polymers to quantum gravity: triple-scaling in rectangular matrix
models
|
Rectangular $N\times M$ matrix models can be solved in several qualitatively
distinct large $N$ limits, since two independent parameters govern the size of
the matrix. Regarded as models of random surfaces, these matrix models
interpolate between branched polymer behaviour and two-dimensional quantum
gravity. We solve such models in a `triple-scaling' regime in this paper, with
$N$ and $M$ becoming large independently. A correspondence between phase
transitions and singularities of mappings from ${\bf R}^2$ to ${\bf R}^2$ is
indicated. At different critical points, the scaling behavior is determined by:
i) two decoupled ordinary differential equations; ii) an ordinary differential
equation and a finite difference equation; or iii) two coupled partial
differential equations. The Painlev\'e II equation arises (in conjunction with
a difference equation) at a point associated with branched polymers. For
critical points described by partial differential equations, there are dual
weak-coupling/strong-coupling expansions. It is conjectured that the new
physics is related to microscopic topology fluctuations.
| 1991-12-16
| 2009-10-22
|
[
"hep-th"
] |
Robert C. Myers and Vipul Periwal
|
hep-th/9112036
|
Ground ring for the 2D NSR string
|
We discuss the BSRT quantization of 2D $N=1$ supergravity coupled to
superconformal matter with $\hat{c} \leq 1$ in the conformal gauge. The
physical states are computed as BRST cohomology. In particular, we consider the
ring structure and associated symmetry algebra for the 2D superstring ($\hat{c}
= 1$).
| 1991-12-16
| 2009-09-11
|
[
"hep-th"
] |
P. Bouwknegt, J. McCarthy and K. Pilch
|
hep-th/9112035
|
The Path Integral for a Particle in Curved Spaces and Weyl Anomalies
|
The computation of anomalies in quantum field theory may be carried out by
evaluating path integral Jacobians, as first shown by Fujikawa. The evaluation
of these Jacobians can be cast in the form of a quantum mechanical problem,
whose solution has a path integral representation. For the case of Weyl
anomalies, also called trace anomalies, one is immediately led to study the
path integral for a particle moving in curved spaces. We analyze the latter in
a manifestly covariant way and by making use of ghost fields. The introduction
of the ghost fields allows us to represent the path integral measure in a form
suitable for performing the perturbative expansion. We employ our method to
compute the Hamiltonian associated with the evolution kernel given by the path
integral with fixed boundary conditions, and use this result to evaluate the
trace needed in field theoretic computation of Weyl anomalies in two
dimensions.
| 1991-12-16
| 2009-10-22
|
[
"hep-th"
] |
Fiorenzo Bastianelli
|
hep-th/9112033
|
States of non-zero ghost number in $c<1$ matter coupled to 2d gravity
|
We study $c<1$ matter coupled to gravity in the Coulomb gas formalism using
the double cohomology of the string BRST and Felder BRST charges. We find that
states outside the primary conformal grid are related to the states of non-zero
ghost number by means of descent equations given by the double cohomology. Some
aspects of the Virasoro structure of the Liouville Fock space are studied. As a
consequence, states of non-zero ghost number are easily constructed by
``solving'' these descent equations. This enables us to map ghost number
conserving correlation functions involving non-zero ghost number states into
those involving states outside the primary conformal grid.
| 1991-12-14
| 2010-11-01
|
[
"hep-th"
] |
S. Govindarajan, T. Jayaraman, V. John and P. Majumdar
|
hep-th/9112030
|
Supersymmetric String Solitons
|
These notes are based on lectures given by C. Callan and J. Harvey at the
1991 Trieste Spring School on String Theory and Quantum Gravity. The subject is
the construction of supersymmetric soliton solutions to superstring theory. A
brief review of solitons and instantons in supersymmetric theories is
presented. Yang-Mills instantons are then used to construct soliton solutions
to heterotic string theory of various types. The structure of these solutions
is discussed using low-energy field theory, sigma-model arguments, and in one
case an exact construction of the underlying superconformal field theory.
| 1991-12-13
| 2007-05-23
|
[
"hep-th"
] |
C.G.Callan Jr., J.A.Harvey and A.E.Strominger
|
hep-th/9112032
|
Multiple Crossover Phenomena and Scale Hopping in Two Dimensions
|
We study the renormalization group for nearly marginal perturbations of a
minimal conformal field theory M_p with p >> 1. To leading order in
perturbation theory, we find a unique one-parameter family of ``hopping
trajectories'' that is characterized by a staircase-like renormalization group
flow of the C-function and the anomalous dimensions and that is related to a
recently solved factorizable scattering theory. We argue that this system is
described by interactions of the form t phi_{(1,3)} - t' \phi_{(3,1)} . As a
function of the relevant parameter t, it undergoes a phase transition with new
critical exponents simultaneously governed by all fixed points M_p, M_{p-1},
..., M_3. Integrable lattice models represent different phases of the same
integrable system that are distinguished by the sign of the irrelevant
parameter t'.
| 1991-12-13
| 2009-10-22
|
[
"hep-th"
] |
Michael Lassig
|
hep-th/9112031
|
From Here to Criticality: Renormalization Group Flow Between Two
Conformal Field Theories
|
Using nonperturbative techniques, we study the renormalization group
trajectory between two conformal field theories. Specifically, we investigate a
perturbation of the A3 superconformal minimal model such that in the infrared
limit the theory flows to the A2 model. The correlation functions in the
topological sector of the theory are computed numerically along the trajectory,
and these results are compared to the expected asymptotic behavior. Excellent
agreement is found, and the characteristic features of the infrared theory,
including the central charge and the normalized operator product expansion
coefficients are obtained. We also review and discuss some aspects of the
geometrical description of N=2 supersymmetric quantum field theories recently
uncovered by S. Cecotti and C. Vafa.
| 1991-12-13
| 2009-10-22
|
[
"hep-th"
] |
W.A. Leaf-Herrmann
|
hep-th/9112027
|
Special geometry, cubic polynomials and homogeneous quaternionic spaces
|
The existing classification of homogeneous quaternionic spaces is not
complete. We study these spaces in the context of certain $N=2$ supergravity
theories, where dimensional reduction induces a mapping between {\em special}
real, K\"ahler and quaternionic spaces. The geometry of the real spaces is
encoded in cubic polynomials, those of the K\"ahler and quaternionic manifolds
in homogeneous holomorphic functions of second degree. We classify all cubic
polynomials that have an invariance group that acts transitively on the real
manifold. The corresponding K\"ahler and quaternionic manifolds are then
homogeneous. We find that they lead to a well-defined subset of the normal
quaternionic spaces classified by \Al\ (and the corresponding special K\"ahler
spaces given by Cecotti), but there is a new class of rank-3 spaces of
quaternionic dimension larger than 3. We also point out that some of the rank-4
\Al\ spaces were not fully specified and correspond to a finite variety of
inequivalent spaces. A simpler version of the equation that underlies the
classification of this paper also emerges in the context of $W_3$ algebras.
| 1991-12-12
| 2009-10-22
|
[
"hep-th"
] |
B. de Wit and A. Van Proeyen
|
hep-th/9112028
|
N=2\ $W$-supergravity
|
We quantise the classical gauge theory of $N=2\ w_\infty$-supergravity and
show how the underlying $N=2$ super-$w_\infty$ algebra gets deformed into an
$N=2$ super-$W_\infty$ algebra. Both algebras contain the $N=2$ super-Virasoro
algebra as a subalgebra. We discuss how one can extract from these results
information about quantum $N=2\ W_N$-supergravity theories containing a finite
number of higher-spin symmetries with superspin $s\le N$. As an example we
discuss the case of quantum $N=2\ W_3$-supergravity.
| 1991-12-12
| 2009-10-22
|
[
"hep-th"
] |
E. Bergshoeff and M. de Roo
|
hep-th/9112029
|
Three-Point Functions of Non-Unitary Minimal Matter Coupled to Gravity
|
The tree-level three-point correlation functions of local operators in the
general $(p,q)$ minimal models coupled to gravity are calculated in the
continuum approach. On one hand, the result agrees with the unitary series
($q=p+1$); and on the other hand, for $p=2, q=2k-1$, we find agreement with the
one-matrix model results.
| 1991-12-12
| 2009-10-22
|
[
"hep-th"
] |
Debashis Ghoshal and Swapna Mahapatra
|
hep-th/9112026
|
Topological Kac-Moody Algebra and Wakimoto Representation
|
It is shown, using the Wakimoto representation, that the level zero SU(2)
Kac-Moody conformal field theory is topological and can be obtained by twisting
an N=2 superconformal theory. Expressions for the associated N=2 superconformal
generators are written down and the Kac-Moody generators are shown to be BRST
exact.
| 1991-12-11
| 2007-05-23
|
[
"hep-th"
] |
Abbas Ali and Alok Kumar
|
hep-th/9112025
|
Aspects of W_\INFTY Symmetry
|
We review the structure of W_\infty algebras, their super and topological
extensions, and their contractions down to (super) w_\infty. Emphasis is put on
the field theoretic realisations of these algebras. We also review the
structure of w_\infty and W_\infty gravities and comment on various
applications of W_\infty symmetry.
| 1991-12-11
| 2007-05-23
|
[
"hep-th"
] |
E. Sezgin
|
hep-th/9112024
|
Recursion relations in semirigid topological gravity
|
A field theoretical realization of topological gravity is discussed in the
semirigid geometry context. In particular, its topological nature is given by
the relation between deRham cohomology and equivariant BRST cohomology and the
fact that all but one of the physical operators are BRST-exact. The puncture
equation and the dilaton equation of pure topological gravity are reproduced,
following reference \dil.
| 1991-12-10
| 2009-10-22
|
[
"hep-th"
] |
Eugene Wong (University of Pennsylvania)
|
hep-th/9112021
|
Puncture Operator in c=1 Liouville Gravity
|
We identify the puncture operator in c=1 Liouville gravity as the discrete
state with spin J=1/2. The correlation functions involving this operator
satisfy the recursion relation which is characteristic in topological gravity.
We derive the recursion relation involving the puncture operator by the
operator product expansion. Multiple point correlation functions are determined
recursively from fewer point functions by this recursion relation.
| 1991-12-10
| 2007-05-23
|
[
"hep-th"
] |
Yoshihisa Kitazawa
|
hep-th/9112023
|
String and Fivebrane Solitons: Singular or Non-singular?
|
We ask whether the recently discovered superstring and superfivebrane
solutions of D=10 supergravity admit the interpretation of non-singular
solitons even though, in the absence of Yang-Mills fields, they exhibit
curvature singularities at the origin. We answer the question using a test
probe/source approach, and find that the nature of the singularity is
probe-dependent. If the test probe and source are both superstrings or both
superfivebranes, one falls into the other in a finite proper time and the
singularity is real, whereas if one is a superstring and the other a
superfivebrane it takes an infinite proper time (the force is repulsive!) and
the singularity is harmless. Black strings and fivebranes, on the other hand,
always display real singularities.
| 1991-12-10
| 2009-10-22
|
[
"hep-th"
] |
M.J. Duff, R.R. Khuri and J.X. Lu
|
hep-th/9112022
|
New fusion rules and $\cR$-matrices for $SL(N)_q$ at roots of unity
|
We derive fusion rules for the composition of $q$-deformed classical
representations (arising in tensor products of the fundamental representation)
with semi-periodic representations of $SL(N)_q$ at roots of unity. We obtain
full reducibility into semi-periodic representations. On the other hand,
heterogeneous $\cR$-matrices which intertwine tensor products of periodic or
semi-periodic representations with $q$-deformed classical representations are
given. These $\cR$-matrices satisfy all the possible Yang Baxter equations with
one another and, when they exist, with the $\cR$-matrices intertwining
homogeneous tensor products of periodic or semi-periodic representations. This
compatibility between these two kinds of representations has never been used in
physical models.
| 1991-12-10
| 2009-10-22
|
[
"hep-th",
"math.QA"
] |
Daniel Arnaudon
|
hep-th/9112019
|
An Introduction to 2d Gravity and Solvable String Models
|
Continuum and discrete approaches to 2d gravity coupled to $c<1$ matter are
reviewed.
| 1991-12-09
| 2008-02-06
|
[
"hep-th"
] |
Emil Martinec
|
hep-th/9112018
|
Superloop Equations and Two Dimensional Supergravity
|
We propose a discrete model whose continuum limit reproduces the string
susceptibility and the scaling dimensions of $(2,4m)$-minimal superconformal
models coupled to $2D$-supergravity. The basic assumption in our presentation
is a set of super-Virasoro constraints imposed on the partition function. We
recover the Neveu-Schwarz and Ramond sectors of the theory, and we are also
able to evaluate all planar loop correlation functions in the continuum limit.
We find evidence to identify the integrable hierarchy of non-linear equations
describing the double scaling limit as a supersymmetric generalization of KP
studied by Rabin.
| 1991-12-09
| 2015-06-26
|
[
"hep-th"
] |
L. Alvarez-Gaume, H. Itoyama, J.L. Manes and A. Zadra
|
hep-th/9112017
|
Universality and Non-Perturbative Definitions of 2D Quantum Gravity from
Matrix Models
|
The universality of the non-perturbative definition of Hermitian one-matrix
models following the quantum, stochastic, or $d=1$-like stabilization is
discussed in comparison with other procedures. We also present another
alternative definition, which illustrates the need of new physical input for
$d=0$ matrix models to make contact with 2D quantum gravity at the
non-perturbative level.
| 1991-12-09
| 2010-11-01
|
[
"hep-th"
] |
J. Luis Miramontes and Joaquin Sanchez Guillen
|
hep-th/9112020
|
Electromagnetic fields of a massless particle and the eikonal
|
Electromagnetic fields of a massless charged particle are described by a
gauge potential that is almost everywhere pure gauge. Solution of quantum
mechanical wave equations in the presence of such fields is therefore immediate
and leads to a new derivation of the quantum electrodynamical eikonal
approximation. The elctromagnetic action in the eikonal limit is localised on a
contour in a two-dimensional Minkowski subspace of four-dimensional space-time.
The exact S-matrix of this reduced theory coincides with the eikonal
approximation, and represents the generalisatin to electrodynamics of the
approach of 't Hooft and the Verlinde's to Planckian scattering.
| 1991-12-09
| 2016-04-20
|
[
"hep-th"
] |
Roman Jackiw, Dan Kabat, Miguel Ortiz
|
hep-th/9112014
|
N=2 Superstrings with (1,2m) Spacetime Signature
|
We show that the $N=2$ superstring in $d=2D\ge6$ real dimensions, with
criticality achieved by including background charges in the two real time
directions, exhibits a ``coordinate-freezing'' phenomenon, whereby the momentum
in one of the two time directions is constrained to take a specific value for
each physical state. This effectively removes this time direction as a physical
coordinate, leaving the theory with $(1,d-2)$ real spacetime signature. Norm
calculations for low-lying physical states suggest that the theory is ghost
free.
| 1991-12-06
| 2009-10-07
|
[
"hep-th"
] |
H. Lu, C.N. Pope, X.J. Wang and K.W. Xu
|
hep-th/9112016
|
Virasoro Action and Virasoro Constraints on Integrable Hierarchies of
the $r$-Matrix Type
|
For a large class of hierarchies of integrable equations admitting a
classical $r-$matrix, we propose a construction for the Virasoro algebra
actionon the Lax operators which commutes with the hierarchy flows. The
construction relies on the existence of dressing transformations associated to
the $r$-matrix and does not involve the notion of a tau function. The
dressing-operator form of the Virasoro action gives the corresponding
formulation of the Virasoro constraints on hierarchies of the $r-$matrix type.
We apply the general construction to several examples which include KP, Toda
and generalized KdV hierarchies, the latter both in scalar and the
Drinfeld-Sokolov formalisms. We prove the consistency of Virasoro action on the
scalar and matrix (Drinfeld-Sokolov) Lax operators, and make an observation on
the difference in the form of string equations in the two formalisms.
| 1991-12-06
| 2007-05-23
|
[
"hep-th"
] |
A.M.Semikhatov
|
hep-th/9112015
|
Model-Building for Fractional Superstrings
|
Fractional superstrings are recently-proposed generalizations of the
traditional superstrings and heterotic strings. They have critical spacetime
dimensions which are less than ten, and in this paper we investigate
model-building for the heterotic versions of these new theories. We concentrate
on the cases with critical spacetime dimensions four and six, and find that a
correspondence can be drawn between the new fractional superstring models and a
special subset of the traditional heterotic string models. This allows us to
generate the partition functions of the new models, and demonstrate that their
number is indeed relatively limited. It also appears that these strings have
uniquely natural compactifications to lower dimensions. In particular, the
fractional superstring with critical dimension six has a natural interpretation
in four-dimensional spacetime.
| 1991-12-06
| 2009-10-22
|
[
"hep-th"
] |
Keith R. Dienes (McGill University) and S.-H. Henry Tye (Cornell
University)
|
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