N=4 Topological Amplitudes and Black Hole Entropy

TL;DR

This paper investigates how N=4 topological string amplitudes influence black hole entropy, identifying a specific operator that corrects entropy calculations and affects the attractor mechanism in string theory models.

Contribution

It identifies a BPS-like operator in N=4 string theory that contributes to black hole entropy corrections at one-loop and influences the attractor equations for moduli.

Findings

The operator corrects the entropy of N=4 black holes at subleading order.

It lifts flat directions in the entropy function for small black holes.

The leading contribution arises at one-loop in heterotic string theory.

Abstract

We study the effects of N=4 topological string amplitudes on the entropy of black holes. We analyse the leading contribution associated to six-derivative terms and find one particular operator which can correct the entropy of N=4 black holes. This operator is BPS-like and appears in the effective action of type II string theory on K3 x T^2 or equivalently its heterotic dual on T^6. In both descriptions the leading contribution arises at one-loop, which we calculate explicitly on the heterotic side. We then consider whether this term has any consequences for the entropy of (large) N=4 black holes and find that it makes indeed a contribution at subleading order. Repeating the computation for small black holes with vanishing horizon area at the classical level, we prove that this coupling lifts certain flat directions in the entropy function thereby being responsible for the attractor equations of some moduli fields.