The AdS_3 boundary energy-momentum tensor, exact in the string length over the curvature radius

摘要

We clarify the map between boundary perturbations of AdS_3 in general relativity, and exactly marginal worldsheet vertex operators in AdS_3 string theory with Neveu-Schwarz Neveu-Schwarz flux. The latter correspond to solutions of the higher derivative low-energy tree level effective action to all orders in the string length over the curvature radius. We calculate the exact expression of the boundary energy-momentum tensor including all these higher derivative corrections in a purely bosonic string theory. The bottom-line is a canonical shift in the normalization of the boundary energy-momentum tensor corresponding to a shift in the curvature radius over the string length squared by the dual Coxeter number of the SL (2, R) subalgebra of the space-time Virasoro algebra. That allows us to propose a value for the Brown-Henneaux central charge including all tree level higher derivative corrections in bosonic string theory, in a scheme dictated by the worldsheet conformal field theory.