PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

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96CHAPTER 5. PARTITION FUNCTIONS OF TORSION > 1 DYONS IN HETEROTIC STRIN
Chapter 6 Concluding Remarks Complete understanding of the microstates of an arbitrary black hole is one the motivations behind a quantum theory of grvity. String theory is the leading candidate for a quantum gravity theory and there is much progress in understanding the microscopics of supersymmetric black holes. In this thesis our aim was to calculate the microscopic degeneracy of Black holes, in N = 4 superstring theory, which preserve 1 -th of the supersymmetries. The formula was known [7] for 4 black holes which carry charges (Q, P ) subject to the condition, g.c.d(Q ∧ P ) = 1 [20, 48, 63]. We extended the result to black holes carrying arbitrary charge vectors. Although we could not provide a first principle derivation of the result, it was done after some time in the reference [85]. There are some aspects of these formulae which require better understanding. We have already seen the appearance of the modular group of the genus two surface, namely Sp(2, Z). The partition function of the theory is given by a modular form of this group or one of its subgroups. But the appearance of Sp(2, Z) is not expected because it is not a symmetry group of the theory. The S-duality group is only a subgroup of this. The first step towards explaining this has been taken in [10, 18]. The contour prescription which we discussed in the introduction can also be derived [84] from the M-theory lift described in the last two papers. It will be very interesting to see how much more can be learned from this picture. 97
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Counting Microscopic Degeneracy of
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Declaration This thesis is a presen
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Acknowledgments Firstly I would lik
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Synopsis Black Holes are classical
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proposed formula reproduces the kno
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Contents 1 Introduction 1 1.1 Broad
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Chapter 1 Introduction Einstein pro
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1.2. D BRANES 3 specific class of s
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1.3. BRIEF INTRODUCTION TO E 8 × E
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1.4. DEGENERACY OF QUARTER-BPS DYON
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1.5. MOTIVATION AND A BRIEF REVIEW
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Chapter 2 Duality orbits, dyon spec
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2.2. T-DUALITY ORBITS OF DYON CHARG
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2.3. AN ALTERNATIVE PROOF 19 Q and
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2.4. PREDICTIONS FOR GAUGE THEORY 2
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2.4. PREDICTIONS FOR GAUGE THEORY 2
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Chapter 3 S-duality Action on Discr
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This proves the desired result. Nex
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For appropriate choice of (α, β,
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Chapter 4 Generalities of Quarter B
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may not be convergent in another re
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35 where Λ is a large positive num
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equiring that we reproduce the blac
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4.1. THE DYON PARTITION FUNCTION 39
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4.2. CONSEQUENCES OF S-DUALITY SYMM
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4.3. CONSTRAINTS FROM WALL CROSSING
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Page 73 and 74: 4.5. EXAMPLES 51 Here k is the same
Page 75 and 76: 4.5. EXAMPLES 53 Next we turn to th
Page 77 and 78: 4.5. EXAMPLES 55 Let us determine t
Page 79 and 80: 4.5. EXAMPLES 57 We shall now set a
Page 81 and 82: 4.5. EXAMPLES 59 uncorrelated and c
Page 83 and 84: 4.5. EXAMPLES 61 is an integer. Sin
Page 85 and 86: 4.5. EXAMPLES 63 1 ((Q−P 2 )/2)2
Page 87 and 88: 4.5. EXAMPLES 65 Finally we turn to
Page 89 and 90: 4.5. EXAMPLES 67 IIB description of
Page 91 and 92: 4.5. EXAMPLES 69 Note that Q and P
Page 93 and 94: 4.5. EXAMPLES 71 On the other hand
Page 95 and 96: 4.6. A PROPOSAL FOR THE PARTITION F
Page 103 and 104: 4.7. REVERSE APPLICATIONS 81 Thus i
Page 105 and 106: 4.7. REVERSE APPLICATIONS 83 For th
Page 107 and 108: Chapter 5 Partition Functions of To
Page 109 and 110: crossing formula for decay into a p
Page 111 and 112: 89 As a consequence of (5.0.19) and
Page 113 and 114: 91 In the primed variables the desi
Page 115 and 116: Furthermore, in order to reproduce
Page 117: The spectrum in gauge theory contai
Page 121 and 122: Bibliography [1] J.Polchinski ”Di
Page 123 and 124: BIBLIOGRAPHY 101 [30] M. Stern and
Page 125 and 126: BIBLIOGRAPHY 103 [63] S. Banerjee a
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PHYS08200604018 Shamik Banerjee - Homi Bhabha National ...

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