A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations

Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in the real and complex domain, given that a suitable and tractable truncation has been found. When aiming for solving these equations in the complex domain, that is, for complex external momenta, one has to deform the integration contour of the radial component in the complex plane of the loop momentum expressed in hyper-spherical coordinates. This has to be done in order to avoid poles and branch cuts in the integrand of the self-energy loop. Since the nature of Dyson-Schwinger equations is such, that they have to be solved in a self-consistent way, one cannot analyze the analytic properties of the integrand after every iteration step, as this would not be feasible. In these proceedings, we suggest a machine learning pipeline based on deep learning (DL) approaches to computer vision (CV), as well as deep reinforcement learning (DRL), that could solve this problem autonomously by detecting poles and branch cuts in the numerical integrand after every iteration step and by suggesting suitable integration contour deformations that avoid these obstructions. We sketch out a proof of principle for both of these tasks, that is, the pole and branch cut detection, as well as the contour deformation.

Quantum Spectral Curve for AdS3/CFT2: a proposal

We conjecture the Quantum Spectral Curve equations for string theory on AdS3× S3× T4 with RR charge and its CFT2 dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS5 and AdS4 cases, but contains a critical new feature — the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.

EFT and the SUSY index on the 2nd sheet

The counting of BPS states in four-dimensional \mathcal{N}=1𝒩=1 theories has attracted a lot of attention in recent years. For superconformal theories, these states are in one-to-one correspondence with local operators in various short representations. The generating function for this counting problem has branch cuts and hence several Cardy-like limits, which are analogous to high-temperature limits. Particularly interesting is the second sheet, which has been shown to capture the microstates and phases of supersymmetric black holes in AdS_55. Here we present a 3d Effective Field Theory (EFT) approach to the high-temperature limit on the second sheet. We use the EFT to derive the behavior of the index at orders \beta^{-2},\beta^{-1},\beta^0β−2,β−1,β0. We also make a conjecture for O(\beta)O(β), where we argue that the expansion truncates up to exponentially small corrections. An important point is the existence of vector multiplet zero modes, unaccompanied by massless matter fields. The runaway of Affleck-Harvey-Witten is however avoided by a non-perturbative confinement mechanism. This confinement mechanism guarantees that our results are robust.

Pentagon functions for scattering of five massless particles

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

Structures of the massive vector boson propagators at finite temperature illuminated by the Goldstone equivalence gauge

Inspired by the Goldstone equivalence gauge, we study the thermal corrections to an originally massive vector boson by checking the poles and branch cuts. We find that part of the Goldstone boson is spewed out from the longitudinal polarization, becoming a branch cut which can be approximated by the “quasi-poles” in the thermal environment. In this case, physical Goldstone boson somehow partly recovers. We also show the Feynmann rules for the “external legs” of these vector boson as well as the recovered Goldstone boson, expecting to simplify the vector boson participated process calculations by adopting the similar “tree-level” logic as in the zero temperature situation. Gauge boson mixing case are also discussed. Similar results are shown in other gauges, especially in the Rξ gauge.

Approximations of Genocchi polynomials of complex order

Approximation formulas for the Genocchi polynomials of complex order are obtained using contour integration with the contour avoiding branch cuts. An alternative expansion is also obtained by expanding a function involving the generating function in a two-point Taylor expansion.