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

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.