Geodesic
AdS3/CFT2 on a Torus in the Sum over Geometries
Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 17-30

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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. 
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     author = {L. O. Chekhov},
     title = {AdS3/CFT2 on a {Torus} in the {Sum} over {Geometries}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {17--30},
     publisher = {mathdoc},
     volume = {146},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a1/}
}
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L. O. Chekhov. AdS3/CFT2 on a Torus in the Sum over Geometries. Teoretičeskaâ i matematičeskaâ fizika, Tome 146 (2006) no. 1, pp. 17-30. http://geodesic.mathdoc.fr/item/TMF_2006_146_1_a1/