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arXiv · 1309.4428

Indefinite theta functions and black hole partition functions

Gabriel Lopes Cardoso·Michele Cirafici·Rogerio Jorge·Suresh Nampuri
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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.

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Gabriel Lopes Cardoso, Michele Cirafici, Rogerio Jorge, Suresh Nampuri. 2014-07-02. Indefinite theta functions and black hole partition functions. https://doi.org/10.1007/jhep02(2014)019

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