Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 7, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP07(2016)032
Keywords
AdS-CFT Correspondence; Black Holes; Holography and condensed matter physics (AdS/CMT); Holography and quark-gluon plasmas
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Funding
- Dutch Ministry of Education, Culture and Science (OCW)
- US Department of Energy [DE-SC0007894]
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We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A numerical evaluation must face the fact that the sum over the quasinormal modes, indexed by momentum and overtone numbers, is divergent. A necessary ingredient is then a regularization scheme to handle the divergent contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. We then discuss the application of such techniques to more complicated spacetimes.
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