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

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.

10 pages, Contribution to the Proceedings of the International Workshop on Higher Spin Gauge Theories, Institute for Advanced Studies, NTU, Singapore, November 4-6, 2015