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.
Highlights
Exist in these theories from which one can extract black hole degeneracies
We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory
After an examination of the role played by the terms that contribute to the divergence in counting single-centered black holes, we propose a regularization of the divergent series by converting the sums into indefinite theta functions following a prescription by Zwegers [11], thereby obtaining fully regulated black hole partitions functions with well defined modular transformation properties
Summary
Upon compactification of the type II string on K3 × T2 physical charges are valued in the lattice Γ6,22 ≃ H2(K3; Z) ⊕ 3 Γ1,1. The dual conformal field theory [14] has a central charge defined by the charge p3 which sets the scale for the AdS3 space; all states in this CFT are labeled as excitations above the vacuum by the quantum number q0 and the angular momentum q1 of the BTZ black hole. This provides a macroscopic partition function which counts single-centered black hole attractor geometries in a statistical ensemble where the pI are held fixed and the qI are summed over.. Definitions and properties of indefinite theta functions are briefly summarized in appendix C
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
