Black Hole Hair Removal For N=4 CHL Models

TL;DR

This paper extends the analysis of black hole hair modes to N=4 CHL models, demonstrating that removing these modes aligns microscopic and horizon partition functions, and provides detailed smoothness analysis for rotating black holes.

Contribution

It identifies hair modes in both untwisted and twisted sectors of N=4 CHL models and shows their removal reconciles microscopic and horizon partition functions, filling a gap in the literature.

Findings

Hair modes identified in untwisted and twisted sectors.

Removing hair modes aligns microscopic and horizon partition functions.

Detailed smoothness analysis for rotating black holes provided.

Abstract

Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.