Indefinite theta functions and black hole partition functions

Abstract

We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions.

35 pages; v2: various comments added; v3: a few typos corrected

References in corpus (7)

• Mock Theta Functions
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Comments on the Spectrum of CHL Dyons
• Dyon Spectrum in Generic N=4 Supersymmetric Z_N Orbifolds
• Two Centered Black Holes and N=4 Dyon Spectrum
• BPS Black Holes
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