A so(2,2) extension of JT gravity via the Virasoro-Kac-Moody semidirect product

TL;DR

This paper extends Jackiw-Teitelboim gravity by incorporating a so(2,2) symmetry via a Virasoro-Kac-Moody algebra, deriving a boundary action that connects to SYK-like models and explores boundary conditions and symmetries.

Contribution

It introduces a novel extension of JT gravity using a Virasoro-Kac-Moody algebra, linking bulk gauge fields with boundary dynamics in a new way.

Findings

Derived a boundary action in terms of coadjoint orbits of Virasoro Kac-Moody group.

Obtained a Schwarzian action with additional edge modes.

Connected the effective low energy action to recent SYK-like tensor models.

Abstract

We consider a bulk plus boundary extension of Jackiw-Teitelboim Gravity (JT) coupled with non-abelian gauge fields. The generalization is performed in the Poisson Sigma Model formulation and it is derived as a dimensional reduction of the AdS3 Chern-Simons theory with WZW boundary terms. We discuss the role of boundary conditions in relation to the symmetries of the boundary dynamics and we show that the boundary action can be written in terms of coadjoint orbits of an appropriate Virasoro Kac-Moody group. We obtain a Schwarzian action and interaction terms with additional edge modes that match the effective low energy action of recent SYK-like tensor models.