Super-W∞ asymptotic symmetry of higher-spin AdS3 supergravity

Abstract

We consider (2+1)-dimensional (N, M)-extended higher-spin anti-de Sitter supergravity and study its asymptotic symmetries. The theory is described by the Chern-Simons action based on a real, infinite-dimensional higher-spin superalgebra. We specify consistent boundary conditions on the higher-spin super-gauge connection corresponding to asymptotically anti-de Sitter spacetimes. We then determine the residual gauge transformations that preserve these asymptotic conditions and compute their Poisson bracket algebra. We find that the asymptotic symmetry is enhanced from the higher-spin superalgebra to some (N,M)-extended super-W(infinity) nonlinear superalgebra. The latter has the same classical central charge as pure Einstein gravity. Special attention is paid to the (1,1)-case. Truncation to the bosonic sector yields the previously found W(infinity) algebra, while truncation to the underlying finite-dimensional superalgebra reproduces the N-extended superconformal algebra (in its nonlinear version for N>2). We discuss string theory realization of these higher-spin anti-de Sitter supergravity theories as well as relations to previous treatments of super-W(infinity) in the literature.