Phases of complex SYK from Euclidean wormholes

Abstract

We present a JT gravity set up that reveals the evidence of (Euclidean) wormhole to black hole phase transitions at finite charge density and or chemical potential. We identify the low temperature gapped phase of the system as the charged wormhole solution that is conjectured to be dual to a two site complex SYK model at finite density. As the temperature of the system is increased, it passes over to a hot SYK phase which is dual to a two black hole system at finite density. Our analysis further reveals the existence of a (two site) Majorana SYK phase right at the critical point of the first order transition which glues the cold and the hot SYK phases together.