Gauging the complex SYK model

A bstract 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 κ = k / N = 0, but broken at κ ≠ 0. In addition, we find that there is maximal chaos for all k .