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Asymptotic Symmetries of Colored Gravity in Three Dimensions

Abstract

Three-dimensional colored gravity refers to nonabelian isospin extension of Einstein gravity. We investigate the asymptotic symmetry algebra of the SU(N)SU(N)-colored gravity in (2+1)-dimensional anti-de Sitter spacetime. Formulated by the Chern-Simons theory with SU(N,N)×SU(N,N)SU(N,N)\times SU(N,N) gauge group, the theory contains graviton, SU(N)SU(N) Chern-Simons gauge fields and massless spin-two multiplets in the SU(N)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 su(N)^\widehat{\mathfrak{su}(N)} Kac-Moody algebra, supplemented by additional generators corresponding to the massless spin-two adjoint matter fields.Comment: 22 pages, published version in JHE

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