New boundary conditions for AdS$_2$

TL;DR

This paper introduces new boundary conditions for AdS$_2$ in Jackiw-Teitelboim gravity, leading to an enhanced symmetry group and a generalized Schwarzian action that connects to the complex SYK model and black hole physics.

Contribution

It proposes novel boundary conditions for AdS$_2$ that extend the symmetry group and derive a generalized Schwarzian boundary action linked to the warped Virasoro group.

Findings

The boundary action reproduces the low-energy complex SYK model dynamics.

The Euclidean path integral relates to the Saad-Shenker-Stanford random matrix ensemble.

The flat space version also yields a simpler ensemble average.

Abstract

We describe new boundary conditions for AdS$_2$ in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to $\r{Diff}(S^1)\ltimes C^\infty(S^1)$ whose breaking to $\r{SL}(2,\R)\times \r{U}(1)$ controls the near-AdS$_2$ dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.