Point mass geometries, spectral flow and AdS₃-CFT₂ correspondence

Abstract

We discuss, in terms of the AdS₃-CFT₂ correspondence, a one-parameter family of (asymptotically AdS₃) conical geometries which are generated by point masses and interpolate between AdS₃ and BTZ space-times. We show that these correspond to spectral flow in N = (4,4) SCFT₂ which interpolate between NS and R sectors. Our method involves representing the conical spaces as solutions of three-dimensional supergravity based on the supergroup SU(1,1|2)× SU(1,1|2). The boundary SCFT we use is based on the D1/D5 system. The correspondence includes comparing the Euclidean free energies between supergravity and SCFT for the family of conical spaces including BTZ black holes, and a concrete proposal for representing the point mass by a vertex operator in the SCFT.