Subleading and non-holomorphic corrections to N=2 BPS black hole entropy

TL;DR

This paper investigates non-holomorphic corrections to N=2 BPS black hole entropy, revealing their relation to topological string corrections and proposing a duality-invariant framework with implications for microstate degeneracies.

Contribution

It provides an explicit evaluation of non-holomorphic corrections in the FHSV model and explores their impact on the black hole entropy and partition functions.

Findings

Non-holomorphic corrections are related but distinct from topological string corrections.

A duality-invariant BPS free energy is constructed.

Predictions for the measure are made based on semiclassical arguments.

Abstract

BPS black hole degeneracies can be expressed in terms of an inverse Laplace transform of a partition function based on a mixed electric/magnetic ensemble, which involves a non-trivial integration measure. This measure has been evaluated for black holes with various degrees of supersymmetry and for N=4 supersymmetric black holes all results agree. It generally receives contributions from non-holomorphic corrections. An explicit evaluation of these corrections in the context of the effective action of the FHSV model reveals that these are related to, but quantitatively different from, the non-holomorphic corrections to the topological string, indicating that the relation between the twisted partition functions of the latter and the effective action is more subtle than has so far been envisaged. The effective action result leads to a duality invariant BPS free energy and arguments are presented for the existence of consistent non-holomorphic deformations of special geometry that can account for these effects. A prediction is given for the measure based on semiclassical arguments for a class of N=2 black holes. Furthermore an attempt is made to confront some of the results of this paper to a recent proposal for the microstate degeneracies of the STU model.