Functional determinants, generalized BTZ geometries and Selberg zeta function

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15 Citations (Scopus)


We continue the study of a special entry in the AdS/CFT dictionary, namely a holographic formula relating the functional determinant of the scattering operator in an asymptotically locally anti-de Sitter space to a relative functional determinant of the scalar Laplacian in the bulk. A heuristic derivation of the formula involves a one-loop quantum effect in the bulk and the corresponding sub-leading correction at large N on the boundary. We presently explore the formula in the background of a higher dimensional version of the Euclidean BTZ black hole, obtained as a quotient of hyperbolic space by a discrete subgroup of isometries generated by a loxodromic (or hyperbolic) element consisting of dilation (temperature) and torsion angles (twist). The bulk computation is done using heat-kernel techniques and fractional calculus. At the boundary, we acquire a recursive scheme that allows us to successively include rotation blocks in spacelike planes in the embedding space. The determinants are compactly expressed in terms of an associated (Patterson-)Selberg zeta function and a connection to quasi-normal frequencies is discussed.

Original languageEnglish
Article number205402
JournalJournal of Physics A: Mathematical and Theoretical
Issue number20
Publication statusPublished - 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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