AdS$_3$ gravity and the complex SYK models

TL;DR

This paper introduces a non conformal boundary condition for AdS3 gravity that relates to warped conformal field theories and results in an effective action near extremality resembling complex SYK models with symmetry breaking.

Contribution

It generalizes CSS boundary conditions to break certain symmetries and connects AdS3 gravity to complex SYK models through an effective action with similar symmetry breaking patterns.

Findings

Boundary conditions break $$ Kac-Moody-Virasoro symmetry to two $u(1)$s.

Effective action near extremality includes Schwarzian and additional symmetry-breaking terms.

Connection established between 3D gravity boundary conditions and complex SYK model dynamics.

Abstract

We provide a non conformal generalization of the Comp\`ere-Song-Strominger (CSS) boundary conditions for AdS$_3$ gravity that breaks the $\widehat u(1)$ Kac-Moody-Virasoro symmetry to two $u(1)$s. The holographic dual specified by the new boundary conditions can be understood as an irrelevant deformation of a warped conformal field theory (WCFT). Upon consistent reduction to two dimensions, AdS$_3$ gravity results in a deformed Jackiw-Teitelboim dilaton gravity model coupled to a Maxwell field. We show that near extremality the boundary conditions inherited from generalized CSS boundary conditions in three dimensions give rise to an effective action exhibiting the same symmetry breaking pattern as the complex Sachdev-Ye-Kitaev models. Besides the Schwarzian term reflecting the breaking of conformal symmetry, the effective action contains an additional term that captures the breaking of the $\widehat u(1)$ Kac-Moody symmetry.