Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity

TL;DR

<3-5 sentence high-level summary> The paper analyzes the asymptotic symmetries of (N,M)-extended higher-spin AdS3 supergravity formulated as Chern-Simons theory with gauge algebras shs^E(N|2,R) ⊕ shs^E(M|2,R). It demonstrates that the asymptotic symmetry group is a nonlinear super-W_∞ algebra with a central charge identical to that of pure Einstein gravity, and shows that the finite shs^E(N|2,R) algebra appears as the wedge subalgebra of this larger structure. It also establishes how AdS3 exact symmetries are embedded within the asymptotic algebra and discusses λ-deformations, extensions to other algebras, string-theory realizations, and potential holographic dual CFTs. The work provides a framework for understanding higher-spin supergravity in AdS3 and its connections to DS reduction and boundary conformal algebras, with implications for holography and quantum aspects of higher-spin dynamics.

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.