Classical single centered solutions of 1/4 BPS dyons in $$ \mathcal{N} $$
 = 4 theories are usually constructed in duality frames which contain non-trivial hair degrees of freedom localized outside the horizon. These modes are in addition to the fermionic zero modes associated with broken supersymmetry. Identifying and removing the hair from the 1/4 BPS index allows us to isolate the degrees of freedom associated with the horizon. The spherical symmetry of the horizon then ensures that index of the horizon states has to be positive. We verify that this is indeed the case for the canonical example of dyons in type IIB theory on K3 × T2 and prove this property holds for a class of states. We generalise this observation to all CHL orbifolds, this involves identifying the hair and isolating the horizon degrees of freedom. We then identify the horizon states for 1/4 BPS dyons in $$ \mathcal{N} $$
 = 4 models obtained by freely acting ℤ2 and ℤ3 orbifolds of type IIB theory compactified on T6 and observe that the index is again positive for single centred black holes. This observation coupled with the fact the 1/4 BPS index of single centred solutions without removal of the hair violates positivity indicates that there exists no duality frame in these models without non-trivial hair.

/pdf/horizon-states-and-the-sign-of-their-index-in-n-mathcal-n-4-lgzkc2ib9j.pdf

Horizon states and the sign of their index in N $$ \mathcal{N} $$ = 4 dyons

Supergravity.- Supersymmetric Gauge Theories.- An Introduction to Duality Symmetries in String Theory.- Les Houches Lectures on Large N Field Theories and Gravity.- D-branes on the Conifold and N = 1 Gauge/Gravity Dualities.- De Sitter Space.- String Compactification with N = 1 Supersymmetry.- Lectures on Open Strings, and Noncommutative Gauge Theories.- Condensates near the Argyres-Douglas Point in SU(2) Gauge Theory with Broken N = 2 Supersymmetry.- Quantum Field Theory with Extra Dimensions.- Special Holonomy Spaces and M-Theory.- Four Dimensional Non-Critical Strings.- U-Opportunities: Why is Ten Equal to Ten?.- Exact Answers to Approximate Questions - Noncommutative dipoles, Open Wilson Lines and UV-IR Duality.- Open-String Models With Broken Supersymmetry.- On A Field Theory of Open Strings, Tachyon Condensation and Closed Strings.- Exceptional Magic.

Unity from duality : gravity, gauge theory and strings = L'unité de la physique fondamentale : gravité, théorie de jauge et cordes : Les Houches, session LXXVI, 30 July-31 August 2001

Positivity of discrete information for CHL black holes

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.

/pdf/black-hole-hair-removal-for-n-4-chl-models-f5v4vcnbfx.pdf

Black hole hair removal for N = 4 CHL models

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.

/pdf/black-hole-hair-removal-for-n-4-chl-models-332jgucbgn.pdf

P. Shanmugapriya

Papers

Black hole hair removal for N = 4 CHL models

Black Hole Hair Removal For N=4 CHL Models