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

TL;DR

This work generalizes the correspondence between microscopic string-state degeneracy and black hole entropy to four-dimensional N=2 supersymmetric string theories. By showing that the Bekenstein-Hawking entropy and the degeneracy-based microscopic entropy agree up to a universal factor (C = 4 for heterotic cases, with analogous constants in CHL and type II theories), the paper extends prior N=4 results to a broader class of compactifications. It demonstrates that the required constant is universal within heterotic theories and within type II theories, underscoring a robust link between microstates and macroscopic entropy across different string frameworks. The exact value of the universal constant hinges on horizon-region sigma-model corrections and remains an open problem for future research. The analysis relies on restricting the N=2 action to a subspace of the N=4 toroidal theory, preserving the relevant S-matrix structure and enabling a consistent comparison of entropies across 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.