PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

Contents
1 Introduction 1
1.1 Broad Overview of Black holes in String Theory . . . . . . . . . . . . . . . . . 2
1.2 D Branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Brief Introduction to E 8 × E 8 Heterotic String Theory . . . . . . . . . . . . . 4
1.3.1 Duality Symmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Degeneracy Of Quarter-BPS Dyonic Black Holes . . . . . . . . . . . . . . . . . 6
1.5 Motivation and A Brief Review of The Work Done . . . . . . . . . . . . . . . 9
2 Duality orbits, dyon spectrum and gauge theory limit of heterotic string
theory on T 6 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 T-duality orbits of dyon charges in heterotic string theory on T 6 . . . . . . . . 13
2.3 An Alternative Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.4 Predictions for gauge theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 S-duality Action on Discrete T-duality Invariants 25
4 Generalities of Quarter BPS Dyon Partition Function 31
4.1 The dyon partition function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Consequences of S-duality symmetry . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Constraints from wall crossing . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Black hole entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5.1 Dyons with unit torsion in heterotic string theory on T 6 . . . . . . . . 51
4.5.2 Dyons with unit torsion and even Q 2 /2 in heterotic on T 6 . . . . . . . 54
4.5.3 Dyons of torsion 2 in heterotic string theory on T 6 . . . . . . . . . . . 60
4.5.4 Dyons in Z 2 CHL orbifold with twisted sector electric charge . . . . . 65
xix