AdS3/CFT2 on a Torus in the Sum over Geometries

We investigate the AdS₃/CFT₂ correspondence for the Euclidean AdS₃ space compactified on a solid torus with the CFT field on the regularizing boundary surface in the bulk. Correlation functions corresponding to the bulk theory at a finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In the sum over geometries in both the regular and the ℤ _N orbifold cases, the two-point correlation function for massless modes transforms into a finite sum of products of the conformal-anticonformal CFT Green's functions up to divergent terms proportional to the volume of the SL(2, ℤ)/ℤ group. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 1, pp. 17–30, January, 2006.