Strings from 3D gravity: asymptotic dynamics of AdS$_3$ gravity with free boundary conditions

TL;DR

This paper demonstrates that three-dimensional AdS gravity with free boundary conditions can be described by a boundary string theory with an AdS$_3$ target space, linking boundary conditions to string Virasoro constraints.

Contribution

It introduces a novel boundary description of AdS$_3$ gravity using string theory, extending previous WZW-based formulations to free boundary conditions.

Findings

Boundary conditions are enforced via string Virasoro constraints.

AdS$_3$ gravity with free boundary conditions is equivalent to a boundary string theory.

The boundary string's target space is also AdS$_3$.

Abstract

Pure three-dimensional gravity in anti-de Sitter space can be formulated as an SL(2,R) $\times $ SL(2,R) Chern-Simons theory, and the latter can be reduced to a WZW theory at the boundary. In this paper we show that AdS$_3$ gravity with free boundary conditions is described by a string at the boundary whose target spacetime is also AdS$_3$. While boundary conditions in the standard construction of Coussaert, Henneaux, and van Driel are enforced through constraints on the WZW currents, we find that free boundary conditions are partially enforced through the string Virasoro constraints.