Spacetime Virasoro algebra from strings on zero radius AdS3

We study bosonic string theory in the light-cone gauge on AdS3 spacetime with zero radius of curvature (in string units) R/ √ α′ = 0. We find that the worldsheet theory admits an infinite number of conserved quantities which are naturally interpreted as spacetime charges and which form a representation of (two commuting copies of) a Virasoro algebra. Near the boundary of AdS3 these charges are found to be isomorphic to the infinite set of asymptotic Killing vectors of AdS3 found originally by Brown and Henneaux. In addition to the spacetime Virasoro algebra, there is a worldsheet Virasoro algebra that generates diffeomorphisms of the spatial coordinate of the string worldsheet. We find that if the worldsheet Virasoro algebra has a central extension then the spacetime Virasoro algebra acquires a central extension via a mechanism similar to that encountered in the context of the SL(2,R) WZW model. Our observations are consistent with a recently proposed duality between bosonic strings on zero radius AdSd+1 and free field theory in d dimensions.