Asymptotic Symmetries of Colored Gravity in Three Dimensions

TL;DR

This paper explores the asymptotic symmetry algebra of three-dimensional colored gravity, revealing a nonlinear extension of Virasoro and Kac-Moody algebras in an anti-de Sitter spacetime setting.

Contribution

It identifies the asymptotic symmetry algebra of $SU(N)$-colored gravity as a nonlinear extension of Virasoro and Kac-Moody algebras, incorporating nonabelian gauge fields and massless spin-two multiplets.

Findings

Derived the asymptotic symmetry algebra as a nonlinear extension of Virasoro and $ ext{Kac-Moody}$ algebras.

Included additional generators for massless spin-two adjoint matter fields.

Extended the understanding of symmetries in colored gravity theories in AdS3.

Abstract

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the $SU(N)$-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with $SU(N,N)\times SU(N,N)$ gauge group, the theory contains graviton, $SU(N)$ Chern-Simons gauge fields and massless spin-two multiplets in the $SU(N)$ adjoint representation, thus extending diffeomorphism to colored, nonabelian counterpart. We identify the asymptotic symmetry as Poisson algebra of generators associated with the residual global symmetries of the nonabelian diffeomorphism set by appropriately chosen boundary conditions. The resulting asymptotic symmetry algebra is a nonlinear extension of Virasoro algeba and $\widehat{\mathfrak{su}(N)}$ Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.