Daily Papers

In this paper, we investigate the quantum behaviour near the classical singularity of a black hole. We describe the black-hole interior by the Kantowski-Sachs metric, with a string propagating in this region. This approach is motivated by the fact that, near the classical singularity, spacetime curvature reaches Planck or string scales, necessitating a description in terms of string-theoretic degrees of freedom. The string dynamics is formulated via the Polyakov action, and the combined system is canonically quantized to derive the corresponding Wheeler-DeWitt equation. Although the equation is separable in the radial and azimuthal string sectors, the remaining geometric and string degrees of freedom are nontrivially coupled. To address this, we employ a perturbative approach and obtain the wave function up to first order. At the zeroth-order, the angular part is described by the general Heun function, while the geometric part is expressed in terms of the Bessel function. The first-order wave function is governed by a source term containing the zeroth-order solution, and we obtain its explicit expression in terms of the complementary function and the particular integral. We confirm regularity of the wave function at both zeroth and first order, at the singularity as well as at the horizon. Regularity at the horizon imposes a discretization condition on one eigenvalue, while another eigenvalue is quantized due to the azimuthal periodicity of the wave function. Importantly, both zeroth- and first-order solutions satisfy the DeWitt boundary condition, implying resolution of the black hole singularity within this quantum framework.

The orbital, spin and valley degrees of freedom in silicon quantum dots support many modes of spin qubit operation. However, it is generally challenging to obtain information about the energy level spectrum over large ranges of parameter space. We demonstrate a form of spectroscopy that is capable of mapping the energy level structure of a double quantum dot as a function of level detuning, interdot tunnel coupling, and magnetic field. In the one electron regime, we directly observe the transition from the atom like energy levels of isolated quantum dots to molecular like bonding and anti bonding states with increasing interdot tunnel coupling. We also resolve the Zeeman splitting of ground and excited valley states in a magnetic field. In the two electron regime, we gain access to the detuning dependent singlet triplet splitting. Our work may be extended to a broader class of systems, such as strong spin-orbit materials or proximitized quantum dots, allowing the direct extraction of various energy gaps.

We construct an exact analytic solution of the revised small-x helicity evolution equations, where the contributions of the quark-to-gluon and gluon-to-quark transition operators were newly included. These evolution equations are written in the large-N_c&N_f limit and are double-logarithmic, resumming powers of alpha_sln^2(1/x). Here N_c and N_f are the numbers of quark colors and flavors, while alpha_s is the strong coupling constant and x is the Bjorken-x variable. Using our solution, we obtain analytic expressions for the flavor singlet quark and gluon helicity parton distribution functions (PDFs) and for the g_1 structure function as double-inverse Laplace transforms. We also extract analytic expressions for the four DGLAP polarized anomalous dimensions Delta gamma_{qq}, Delta gamma_{qG}, Delta gamma_{Gq}, and Delta gamma_{GG}: these expressions resum powers of alpha_s/omega^2 to all orders at large-N_c&N_f (with omega the Mellin moment variable). We extract the leading small-x growth of the helicity distributions, align \Delta\Sigma(x,Q^2) \sim \Delta G(x,Q^2)\sim g_1(x,Q^2) \sim \left(1{x}\right)^{\alpha_h}, align where the intercept alpha_h satisfies an algebraic equation. We determine alpha_h numerically for various values of N_c and N_f. We further obtain the explicit asymptotic expressions for the helicity distributions, which yield numerical values for the ratio of the gluon helicity PDF to the flavor singlet quark helicity PDF in the small-x asymptotic limit (for different N_f/N_c). We find that all our predictions for polarized DGLAP anomalous dimensions are fully consistent with the existing finite-order calculations. Similar to the large-N_c case, our intercept alpha_h exhibits a very slight disagreement with the predictions made within the infrared evolution equations framework.

Single-minus tree-level n-gluon scattering amplitudes are reconsidered. Often presumed to vanish, they are shown here to be nonvanishing for certain "half-collinear" configurations existing in Klein space or for complexified momenta. We derive a piecewise-constant closed-form expression for the decay of a single minus-helicity gluon into n-1 plus-helicity gluons as a function of their momenta. This formula nontrivially satisfies multiple consistency conditions including Weinberg's soft theorem.

There exist a number of well known multiplicative generating functions for series of Schur functions. Amongst these are some related to the dual Cauchy identity whose expansion coefficients are rather simple, and in some cases periodic in parameters specifying the Schur functions. More recently similar identities have been found involving expansions in terms of characters of the symplectic group. Here these results are extended and generalised to all classical Lie groups. This is done through the derivation of explicit recurrence relations for the expansion coefficients based on the action of the Weyl groups of both the symplectic and orthogonal groups. Copious results are tabulated in the form of explicit values of the expansion coefficients as functions of highest weight parameters. An alternative approach is then based on dual pairs of symplectic and/or orthogonal groups. A byproduct of this approach is that expansions in terms of spin orthogonal group characters can always be recovered from non-spin cases.

We establish a unified framework for understanding the results on the Weil quadratic form obtained by Yoshida (1992), Bombieri (2001, 2003), Connes--Consani (2023), and Connes--Consani--Moscovici (2025+) from the perspective of the screw function introduced in Suzuki (2023). An advantage of the approach via the screw function is that it provides a method to study the Weil quadratic form, which is originally defined in terms of distributions, by means of continuous functions. Based on this framework, we formulate a conjecture stating that a self-adjoint operator whose eigenvalues are the imaginary parts of the nontrivial zeros of the Riemann zeta function can be obtained as the limit, as a to infty, of self-adjoint operators arising from nonlocal realizations of the first-order differential operator on the finite interval [-a,a]. All these results are obtained without assuming the Riemann Hypothesis. This conjecture may be compared with the limit formula for the Riemann zeta function expressed in terms of zeta-regularized products proposed by Connes, Consani, and Moscovici, and it sheds new light on the spectral-theoretic interpretation of the nontrivial zeros of the Riemann zeta function.