N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

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70 Conclusions and Outlook likely to exist only in harmonic superspace, which admits unconstrained prepotentials for N = 2 vector multiplets that could serve as the necessary auxiliary superfields. In fact, the superfield constraints we have found in this thesis can readily be converted into constraints on a corresponding harmonic superfield, cf. [2]. However, presumably the 2-forms have to be embedded in other multiplets than the ones of the vector-tensor variety, since the latter always introduce in addition as many vectors as there are tensors, which is likely to prevent a formulation of pure Freedman-Townsend models. The only other multiplet known to include a 2-form gauge field (apart from the yet to be constructed double-tensor multiplet which, as the name suggests, would hardly be an alternative) is the so-called tensor multiplet [7] we have encountered briefly in section 1.2. Finally, we note that also the purely bosonic Henneaux-Knaepen models deserve further study concerning a possible extension of the Chern-Simons couplings. As has been shown in the last chapter, the gauge field part of the nonlinear vector-tensor multiplet <strong>with</strong> local central charge hints at a generalization that exceeds the one included already in [28] and in our exposition of the models in section 3.5.
Appendix A Conventions A.1 Vectors and Spinors We denote Lorentz vector indices as usual by small letters from the middle of the greek alphabet, while those from the beginning are reserved for two-component Weyl spinors, which are used exclusively in this thesis. Small letters from the middle of the latin alphabet denote SU(2) spinors in the fundamental representation and run also from 1 to 2. The signature of the Minkowski metric follows the convention in particle physics, ηµν = diag (1, −1, −1, −1) . (A.1) Parantheses and square brackets denote symmetrization and antisymmetrization of the enclosed indices respectively, V(A1...An) = 1 n! V[A1...An] = 1 n! π∈Sn VA π(1)...A π(n) (A.2) sgn(π) VAπ(1)...A , (A.3) π(n) π∈Sn where A ∈ {µ, α, ˙α, i}. The Levi-Civita tensor ε A1...Ad is antisymmetric upon interchange of any two indices, and the following relations hold, εA1...Ad = ηA1B1 . . . ηAdBd εB1...Bd , ηAB = diag (1, −1, . . . , −1) (A.4) ε 0...(d−1) = 1 , ε0...(d−1) = (−) d−1 εA1...Ad εB1...Bd = (−) d−1 d! δ [B1 (A.5) . . . δ A1 Bd] . (A.6) The Hodge dual of an antisymmetric Lorentz tensor is denoted by a tilde, Ad ˜F µν = 1 2 εµνρσ Fρσ . (A.7) Our conventions concerning Weyl spinors agree <strong>with</strong> those in [29]. Indices are raised and lowered by means of the ε-tensors according to ψ α = ε αβ ψβ , ψα = εαβψ β 71 (A.8)
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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
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Introduction Despite the lack of ex
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Chapter 1 Gauging the Central Charg
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1.1. The N=2 Supersymmetry Algebra
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1.1. The N=2 Supersymmetry Algebra
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1.2. The Linear Multiplet 9 1.2 The
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1.2. The Linear Multiplet 11 It wil
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1.3. The Hypermultiplet 13 second e
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1.3. The Hypermultiplet 15 so in th
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18 Chapter 2. The Vector-Tensor Mul
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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 and 64: 3.5. Henneaux-Knaepen Models 55 whe
Page 65 and 66: Chapter 4 The Nonlinear Case In sec
Page 73 and 74: 4.3. The Lagrangian 65 This of cour
Page 75: 4.3. The Lagrangian 67 which introd
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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