Holographic chiral induced W-gravities

Abstract

We study boundary conditions for 3-dimensional higher spin gravity that admit asymptotic symmetry algebras expected of 2-dimensional induced higher spin theories in the light-cone gauge. For the higher spin theory based on $$ sl\left(3,\mathbb{R}\right)\oplus sl\left(3,\mathbb{R}\right) $$ algebra, our boundary conditions give rise to one copy of classical W 3 and a copy of $$ sl\left(3,\mathbb{R}\right) $$ or su(1, 2) Kac-Moody as the asymptotic symmetry algebra. We propose that the higher spin theories with these boundary conditions describe appropriate chiral induced W-gravity theories on the boundary. We also consider boundary conditions of spin-3 higher spin gravity that admit a u(1) ⊕ u(1) current algebra.