Quantum black holes, elliptic genera and spectral partition functions

A. A. Bytsenko, M. Chaichian, R. J. Szabo, A. Tureanu

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lies in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi-Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.

Original languageEnglish
Article number1450048
Number of pages42
JournalInternational Journal of Geometric Methods in Modern Physics
Volume11
Issue number5
DOIs
Publication statusPublished - May 2014

Keywords

  • Black holes
  • D-branes
  • Elliptic genera
  • Hyperbolic manifolds

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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