AdS_3/CFT_2 on torus in the sum over geometries

Details AdS_3/CFT_2 on torus in the sum over geometries AdS_3/CFT_2 on torus in the sum over geometries

2004-09-10

arxiv.org/abs/hep-th/0409113v1

Theor.Math.Phys. 146 (2006) 13-24; Teor.Mat.Fiz. 146 (2006) 17-30

Physics

High Energy Physics

High Energy Physics - Theory

11 pages in LaTeX, 1 figure

Scientific paper

We investigate the AdS$_3$/CFT$_2$ correspondence for the Euclidean AdS$_3$ 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 finite temperature tend to the standard CFT correlation functions in the limit of removed regularization. In both regular and $Z_N$ orbifold cases, in the sum over geometries, the two-point correlation function for massless modes factors, up to divergent terms proportional to the volume of the $SL(2,Z)/Z}$ group, into the finite sum of products of the conformal--anticonformal CFT Green's functions.

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