Black Holes, Elementary Strings and Holomorphic Anomaly

TL;DR

This paper extends the understanding of black hole entropy in N=4 heterotic string theory by demonstrating that accounting for holomorphic anomaly corrections aligns black hole entropy with string state degeneracies across various compactifications.

Contribution

It generalizes previous results by showing the agreement between black hole entropy and string degeneracy holds for multiple N=4 heterotic compactifications when holomorphic anomaly corrections are included.

Findings

Agreement between black hole entropy and string degeneracy for various compactifications

Holomorphic anomaly corrections are essential for accurate entropy calculations

Results support the universality of the entropy-degeneracy relation in N=4 theories

Abstract

In a previous paper we had proposed a specific route to relating the entropy of two charge black holes to the degeneracy of elementary string states in N=4 supersymmetric heterotic string theory in four dimensions. For toroidal compactification this proposal works correctly to all orders in a power series expansion in inverse charges provided we take into account the corrections to the black hole entropy formula due to holomorphic anomaly. In this paper we demonstrate that similar agreement holds also for other N=4 supersymmetric heterotic string compactifications.