Functional determinants, index theorems, and exact quantum black hole entropy

Sameer Murthy, Valentin Reys

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)
119 Downloads (Pure)

Abstract

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 18 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.
Original languageEnglish
Pages (from-to)1-41
JournalJournal of High Energy Physics
Early online date4 Dec 2015
DOIs
Publication statusPublished - Dec 2015

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