Quantum black holes, elliptic genera and spectral partition functions

Author:

Bytsenko A. A.1,Chaichian M.2,Szabo R. J.345,Tureanu A.2

Affiliation:

1. Departamento de Física, Universidade Estadual de Londrina, Caixa Postal 6001, Londrina-Paraná, Brazil

2. Department of Physics, University of Helsinki, P. O. Box 64, FI-00014 Helsinki, Finland

3. Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS, UK

4. Maxwell Institute for Mathematical Sciences, Edinburgh, UK

5. The Tait Institute, Edinburgh, UK

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

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