N=2 Supersymmetric Gauge Theories with Nonpolynomial Interactions

74 Appendix A. Conventions
σ µν αβ σµν γδ = −2 εα(γ εδ)β , σ µν α β ¯σµν ˙γ ˙ δ = 0 . (A.35)
These identities imply among others the following two useful relations: Let Fµν, Gµν,
Hµν be antisymmetric tensors and Vµ, Wµ be vectors. Then one has
Fα β Gβ α + ¯ F ˙α ˙ β ¯ H ˙ β ˙α = i ˜ F µν (Gµν − Hµν) − F µν (Gµν + Hµν) (A.36)
Fα β Vβ ˙α + W α ˙ β ¯ F ˙ β ˙α = iσ µ
α ˙α ˜ Fµν(V ν − W ν ) − σ µ
α ˙α Fµν(V ν + W ν ) . (A.37)
A.3 Multiplet Components
In the course of the present thesis we encounter numerous supersymmetry multiplets.
For quick reference we now list their components. As explained in section 1.1 the corresponding
superfields are labeled by the same letter as used for the lowest component
(if there are several components of the same dimension, the first in the respective list
provides the superfield label). Symbols separated by a semicolon denote field strengths.
Components of the vector-tensor multiplet:
L , Vµ , Bµν , ψ i α , U ; Gµν , W µ ; Vµν , H µ .
Components of the central charge vector multiplet:
Z , ¯ Z , Aµ , λ i α , Y ij ; Fµν .
Components of additional vector multiplets:
Components of the linear multiplet:
Components of the hypermultiplet:
φ I , ¯ φ I , A I µ , χ I α , D ijI ; F I µν .
ϕ ij (L ij ) , ϱ i α , S , ¯ S , K µ .
ϕ i , ¯ϕi , χ α , ¯ ψ ˙α , F i , ¯ Fi .