Indefinite theta functions for counting attractor backgrounds
Date
2014-10-03
Authors
Cardoso, Gabriel Lopes
Ciraficia, Michele
Nampurib, Suresh
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
In this note, we employ indefinite theta functions to regularize canonical partition functions for single-center dyonic BPS black holes. These partition functions count dyonic degeneracies in the Hilbert space of four-dimensional toroidally compactified heterotic string theory, graded by electric and magnetic charges. The regularization is achieved by viewing the weighted sums of degeneracies as sums over charge excitations in the near-horizon attractor geometry of an arbitrarily chosen black hole background, and eliminating the unstable modes. This enables us to rewrite these sums in terms of indefinite theta functions. Background independence is then implemented by using the transformation property of indefinite theta functions under elliptic transformations, while modular transformations are used to make contact with semi-classical results in supergravity.
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Keywords
Research Subject Categories::NATURAL SCIENCES::Physics, Supersymmetry and Duality, Black Holes in String Theory, Extended Supersymmetry, Black Holes