Black holes and Elementary String States in N=2 Supersymmetric String Theories

TL;DR

This paper demonstrates that the microscopic degeneracy of BPS states and the black hole entropy in N=2 supersymmetric string theories match up to a constant, similar to N=4 theories, indicating a universal agreement without new identities.

Contribution

It shows that the entropy matching in N=2 theories is consistent with N=4 theories, revealing a universal aspect of string/black hole entropy correspondence.

Findings

Degeneracy and entropy match up to an undetermined constant.

The constant is identical in N=2 and N=4 theories.

The agreement extends to type II string compactifications.

Abstract

We compare the logarithm of the degeneracy of BPS saturated elementary string states and the string modified Bekenstein-Hawking entropy of the corresponding black holes in N=2 supersymmetric heterotic string compactification to four dimensions. As in the case of N=4 supersymmetric theory, the two results match up to an overall undetermined numerical factor. We also show that this undetermined numerical constant is identical in the N=2 and N=4 supersymmetric theories, therby showing that the agreement between the Bekenstein-Hawking entropy and the microscopic entropy for N=2 theories does not require any new identity, other than the one already required for the N=4 theory. A similar result holds for type II string compactification as well.