Classical and quantum N=2 supersymmetric black holes

TL;DR

This paper investigates quantum and classical N=2 supersymmetric black holes in heterotic and type-II string theories, deriving new entropy formulas and exploring conditions for finite entropy with relaxed charge constraints.

Contribution

It introduces new entropy/area formulas for black holes in heterotic and type-II compactifications, accounting for quantum corrections and topological data.

Findings

Perturbative corrections replace coupling constants in entropy formulas for heterotic black holes.

New entropy/area formula for type-II black holes depends on topological invariants.

Finite entropy possible even with some charges vanishing, relaxing usual conditions.

Abstract

We use heterotic/type-II prepotentials to study quantum/classical black holes with half the $N=2, D=4$ supersymmetries unbroken. We show that, in the case of heterotic string compactifications, the perturbatively corrected entropy formula is given by the tree-level entropy formula with the tree-level coupling constant replaced by the perturbative coupling constant. In the case of type-II compactifications, we display a new entropy/area formula associated with axion-free black-hole solutions, which depends on the electric and magnetic charges as well as on certain topological data of Calabi--Yau three-folds, namely the intersection numbers, the second Chern class and the Euler number of the three-fold. We show that, for both heterotic and type-II theories, there is the possibility to relax the usual requirement of the non-vanishing of some of the charges and still have a finite entropy.