Fractional Branes and the Entropy of 4D Black Holes

TL;DR

This paper analyzes the microscopic entropy of 4D extremal black holes in type IIB string theory, incorporating fractional branes and ALE space effects, revealing the importance of open strings between fractional D-branes.

Contribution

It introduces a detailed calculation of black hole entropy considering fractional branes on ALE spaces, extending previous models to include arbitrary monopole numbers.

Findings

Complete Bekenstein-Hawking entropy expression derived

Massless open strings between fractional branes are crucial

Black hole sector corresponds to a mixed Higgs-Coulomb branch

Abstract

We reconsider the four dimensional extremal black hole constructed in type IIB string theory as the bound state of D1-branes, D5-branes, momentum, and Kaluza-Klein monopoles. Specifically, we examine the case of an arbitrary number of monopoles. Consequently, the weak coupling calculation of the microscopic entropy requires a study of the D1-D5 system on an ALE space. We find that the complete expression for the Bekenstein-Hawking entropy is obtained by taking into account the massless open strings stretched between the fractional D-branes which arise in the orbifold limit of the ALE space. The black hole sector therefore arises as a mixed Higgs-Coulomb branch of an effective 1+1 dimensional gauge theory.