N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

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56 Chapter 3. The Linear Case together with the choice T a 1 b = 0 0 1 0 , cab = 0 , (3.106) which conforms to f11 1 = 0 for a single antisymmetric tensor. When substituted in eqs. (3.103), (3.104), these coefficients yield the expressions H µ = H µ + gF µν2 A 1 ν , K µν = η µν (1 − g 2 A ρ1 A 1 ρ) + g 2 A µ1 A ν1 K −1 µν = ηµν − g 2 A 1 µA 1 ν 1 − g 2 A 1ρ A 1 ρ which coincide exactly with their counterparts in the supersymmetric model after replacing the scalars by their background values. At last we point out that what made the construction of the bosonic Henneaux-Knaepen models possible in the first place was the introduction of auxiliary fields, resulting in polynomial actions and transformations (a feature shared by the N = 1 supersymmetric versions in [28]). As yet, we do not know how to do this in the N = 2 supersymmetric case. ,
Chapter 4 The Nonlinear Case In section 2.3.2 we have argued that there exist two inequivalent sets of constraints describing the vector-tensor multiplet. So far, we have been dealing only with the first one and its generalizations to admit couplings to vector multiplets. We shall now show how the second set gives rise to a new feature, namely self-interactions of the vector-tensor multiplet. As announced, this will be done from the beginning in the presence of a gauged central charge, but in somewhat less detail than in the previous chapter, for the steps from the constraints to the Bianchi identities and ultimately to the Lagrangian are essentially the same. From the latter in particular we give only the purely bosonic part, as we are mostly interested in the gauge field interactions. 4.1 Consistent Constraints Let us resume the evaluation of the consistency conditions in section 2.3.3. We recall the second solution to eq. 4) of the system of differential equations (2.79), 1 F = − L + h(Z, ¯ Z) We now continue by solving eq. 5) for A, , h real. A + 2 Z = 2 ¯ F ∂ ¯ F = − 2∂h L + h . (4.1) Then it can easily be checked that also eqs. 1) and 19) hold identically. When put into eq. 9), we obtain a condition on h, namely From eq. 10) follows another condition, 0 = ∂A − 1 2 A2 = − 2 L + h which allows to determine h completely, h = ϱ Z + ¯ϱ ¯Z ¯∂∂h = 0 . (4.2) ∂ 2 h + 2 Z ∂h , (4.3) + µ , ϱ ∈ C , µ ∈ R . (4.4) 57
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N=2 Supersymmetric Gauge Theories w
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Abstract In this thesis the central
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Acknowledgments I would like to exp
Page 9 and 10:
Introduction Despite the lack of ex
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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
Page 59 and 60: 3.4. Chern-Simons Couplings 51 Here
Page 61 and 62: 3.5. Henneaux-Knaepen Models 53 eq.
Page 63: 3.5. Henneaux-Knaepen Models 55 whe
Page 73 and 74: 4.3. The Lagrangian 65 This of cour
Page 75: 4.3. The Lagrangian 67 which introd
Page 78 and 79: 70 Conclusions and Outlook likely t
Page 80 and 81: 72 Appendix A. Conventions and the
Page 82 and 83: 74 Appendix A. Conventions σ µν
Page 84 and 85: 76 References [20] N. Dragon and S.
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N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

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