N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

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Acknowledgments I would like to express my gratitude to my advisor Prof. Dr. Norbert Dragon for his support and for giving me so much freedom yet offering guidance when needed. Furthermore, I am greatly indebted to Dr. Sergei Kuzenko and Dr. Friedemann Brandt, with whom I had the pleasure of collaborating during the last two years. Many thanks also to Prof. Dr. Olaf Lechtenfeld for all his efforts concerning the Graduiertenkolleg. Finally, thanks to Jens Reinbach for putting up with me occupying the computer in our office over four months.
Contents Introduction 1 1 Gauging the Central Charge 3 1.1 The N=2 Supersymmetry Algebra . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Linear Multiplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 The Hypermultiplet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2 The Vector-Tensor Multiplet 17 2.1 Introducing the Multiplet . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.2 Consistent Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 The Ansatz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 Invariant Actions . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3.2 Solutions for Z = i . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.3 Generalization to Z(x) . . . . . . . . . . . . . . . . . . . . . . . 32 3 The Linear Case 37 3.1 Consistent Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Transformations and Bianchi Identities . . . . . . . . . . . . . . . . . . 39 3.3 The Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4 Chern-Simons Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . 49 3.5 Henneaux-Knaepen Models . . . . . . . . . . . . . . . . . . . . . . . . 53 4 The Nonlinear Case 57 4.1 Consistent Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Transformations and Bianchi Identities . . . . . . . . . . . . . . . . . . 59 4.3 The Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Conclusions and Outlook 69 A Conventions 71 A.1 Vectors and Spinors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 A.2 σ-Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 A.3 Multiplet Components . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 References 75
Page 1 and 2: N=2 Supersymmetric Gauge Theories w
Page 3: Abstract In this thesis the central
Page 9 and 10: Introduction Despite the lack of ex
Page 11 and 12: Chapter 1 Gauging the Central Charg
Page 13 and 14: 1.1. The N=2 Supersymmetry Algebra
Page 15 and 16: 1.1. The N=2 Supersymmetry Algebra
Page 17 and 18: 1.2. The Linear Multiplet 9 1.2 The
Page 19 and 20: 1.2. The Linear Multiplet 11 It wil
Page 21 and 22: 1.3. The Hypermultiplet 13 second e
Page 23: 1.3. The Hypermultiplet 15 so in th
Page 26 and 27: 18 Chapter 2. The Vector-Tensor Mul
Page 45 and 46: Chapter 3 The Linear Case In this c
Page 47 and 48: 3.2. Transformations and Bianchi Id
Page 53 and 54: 3.3. The Lagrangian 45 7) 0 = ∂
Page 55 and 56: 3.3. The Lagrangian 47 compute the
Page 57 and 58:
3.4. Chern-Simons Couplings 49 To c
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3.4. Chern-Simons Couplings 51 Here
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3.5. Henneaux-Knaepen Models 53 eq.
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3.5. Henneaux-Knaepen Models 55 whe
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Chapter 4 The Nonlinear Case In sec
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4.2. Transformations and Bianchi Id
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4.3. The Lagrangian 65 This of cour
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4.3. The Lagrangian 67 which introd
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70 Conclusions and Outlook likely t
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72 Appendix A. Conventions and the
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74 Appendix A. Conventions σ µν
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76 References [20] N. Dragon and S.
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N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

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