### Abstract

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 sub-leading 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 a 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.

Original language | English |
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Article number | 365401 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 36 |

DOIs | |

Publication status | Published - 23 Nov 2009 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)