Gauging the complex SYK model

TL;DR

This paper studies the gauged complex SYK model with a Wilson line, revealing how gauge field integration affects solutions, symmetry breaking, and chaos, with implications for black hole models in string theory.

Contribution

It introduces the analysis of gauged complex SYK models with Wilson lines, showing how gauge fixing influences low-energy behavior and chaos, extending previous SYK studies.

Findings

Conformal symmetry is preserved at zero charge density.

Symmetry is broken at non-zero charge density.

Maximal chaos persists for all charge values.

Abstract

Motivated by SYK-like models describing near-BPS black holes in string/M-theory, we consider gauging the U$(1)$ symmetry of the complex SYK model in the presence of a Wilson line with charge $k$. At a fixed background gauge field, solutions to the Schwinger-Dyson equations display vastly different properties from those at a fixed real chemical potential. In the partition function and the two-point function, the integral over the gauge field is performed either directly or via a large $N$ saddle point approximation, and both results are consistent with exact diagonalization data. From the behaviour of the two-point function at large $N$, we deduce that the conformal symmetry at low energies is preserved at fixed $\kappa = k/N = 0$, but broken at $\kappa\neq 0$. In addition, we find that there is maximal chaos for all $k$.