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TMF, 2006, Volume 146, Number 1, Pages 17–30 (Mi tmf2005)  

AdS3/CFT2 on a Torus in the Sum over Geometries

L. O. Chekhovab

a Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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 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 $\mathbb Z_N$ 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 $SL(2,\mathbb Z)/\mathbb Z$ group.

Keywords: hyperbolic spaces, Green's function, orbifolds

DOI: https://doi.org/10.4213/tmf2005

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English version:
Theoretical and Mathematical Physics, 2006, 146:1, 13–24

Bibliographic databases:

Document Type: Article

Citation: L. O. Chekhov, “AdS3/CFT2 on a Torus in the Sum over Geometries”, TMF, 146:1 (2006), 17–30; Theoret. and Math. Phys., 146:1 (2006), 13–24

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