Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity

TL;DR

This paper explores the asymptotic symmetry algebra of three-dimensional higher spin anti-de Sitter gravity, revealing a nonlinear W(infinity) algebra with potential implications for quantum gravity and string theory.

Contribution

It demonstrates that the asymptotic symmetry algebra of higher spin AdS gravity is a nonlinear W(infinity) algebra with classical central charges, expanding understanding of boundary symmetries.

Findings

Asymptotic symmetry algebra is a nonlinear W(infinity) algebra.

Boundary conditions lead to a deformed algebra with classical central charges.

Results have implications for quantum gravity and string theory.

Abstract

We investigate the asymptotic symmetry algebra of (2+1)-dimensional higher spin, anti-de Sitter gravity. We use the formulation of the theory as a Chern-Simons gauge theory based on the higher spin algebra hs(1,1). Expanding the gauge connection around asymptotically anti-de Sitter spacetime, we specify consistent boundary conditions on the higher spin gauge fields. We then study residual gauge transformation, the corresponding surface terms and their Poisson bracket algebra. We find that the asymptotic symmetry algebra is a nonlinearly deformed W(infinity) algebra with classical central charges. We discuss implications of our results to quantum gravity and to various situations in string theory.