The sky is the limit: free boundary conditions in AdS$_3$ Chern-Simons theory

TL;DR

This paper investigates free boundary conditions in AdS$_3$ Chern-Simons theory, revealing a boundary string theory with ghost-eliminating Virasoro constraints, and explores implications for higher spin theories.

Contribution

It introduces new diffeomorphism invariant boundary terms in SL(2,R) Chern-Simons theory, enabling free AdS$_3$ boundary conditions and connecting to a boundary string theory.

Findings

Boundary conditions lead to a boundary string theory in AdS$_3$

Virasoro constraints can eliminate ghosts in the boundary theory

Potential generalizations to higher spin theories are discussed

Abstract

We test the effects of new diffeomorphism invariant boundary terms in SL(2,R)$\times$SL(2,R) Chern-Simons theory. The gravitational interpretation corresponds to free AdS$_3$ boundary conditions, without restrictions on the boundary geometry. The boundary theory is the theory of a string in a target AdS$_3$. Its Virasoro conditions can eliminate ghosts. Generalisations to SL(N,R)$\times$SL(N,R) higher spin theories and many other questions are still unexplored.