Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-12-11
J.Phys.A42:365401,2009
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, published JPA version
Scientific paper
10.1088/1751-8113/42/36/365401
A 'holographic formula' expressing the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter(ALAdS) space has been proposed in terms of a relative functional determinant of the scalar Laplacian in the bulk. It stems from considerations in AdS/CFT correspondence of a quantum correction to the partition function in the bulk and the corresponding subleading correction at large N on the boundary. In this paper we probe this prediction for a class of quotients of hyperbolic space by a discrete subgroup of isometries. We restrict to the simplest situation of an abelian group where the quotient geometry describes thermal AdS and also the non-spinning BTZ instanton. The bulk computation is explicitly done using the method of images and the answer can be encoded in a (Patterson-)Selberg zeta-function.
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