More on Complex Sachdev-Ye-Kitaev Eternal Wormholes

TL;DR

This paper explores a generalized complex SYK model with charge conservation, revealing a transition from an eternal wormhole ground state to a black hole phase at higher chemical potentials, and analyzes its dynamics.

Contribution

It introduces a charge-conserving complex SYK model with coupled systems, deriving Green's functions, IR parameters, and the Schwarzian action, and compares analytical and numerical results.

Findings

Ground state is an eternal wormhole at low chemical potential.

System transitions to a black hole phase at higher chemical potential.

Analytical predictions agree with numerical simulations.

Abstract

In this work, we study a generalization of the coupled Sachdev-Ye-Kitaev (SYK) model with $U(1)$ charge conservations. The model contains two copies of the complex SYK model at different chemical potentials, coupled by a direct hopping term. In the zero-temperature and small coupling limit with small averaged chemical potential, the ground state is an eternal wormhole connecting two sides, with a specific charge $Q=0$, which is equivalent to a thermofield double state. We derive the conformal Green's functions and determine corresponding IR parameters. At higher chemical potential, the system transit into the black hole phase. We further derive the Schwarzian effective action and study its quench dynamics. Finally, we compare numerical results with the analytical predictions.