Abstract
The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet. We construct the transformations of this multiplet for mathcal{N} = 3, D = 4. The construction is based on a supersymmetry truncation from the mathcal{N} = 4 Weyl multiplet, on coupling with a current multiplet, and on the implementation of a soft algebra at the nonlinear level, extending mathfrak{s}mathfrak{u} (2, 2|3). This is the first step towards a superconformal calculus for mathcal{N} = 3, D = 4.
Highlights
The main ingredient for local superconformal methods is the multiplet of gauge fields: the Weyl multiplet
The construction is based on a supersymmetry truncation from the N = 4 Weyl multiplet, on coupling with a current multiplet, and on the implementation of a soft algebra at the nonlinear level, extending su(2, 2|3)
An old argument says that N = 3 rigid supersymmetry theories always have a fourth supersymmetry, and are N = 4 supersymmetric theories
Summary
4, is set to zero and secondly the appropriate field components of the N = 4 Weyl multiplet will have to be found that keep an N = 3 symmetry after the truncation. It is useful to record the inverse of the transformation between the ξ symbols: ξkij = εij ξk − 2δk[iξj] This is a multiplet with 64 + 64 components and is found to be in the 8 representation of the SU(3) R-symmetry group. To find the supersymmetry variations we follow the same procedure as was applied in the case of N = 4 conformal supergravity This means that first the linear variations are determined by imposing invariance of the first order action, and inserting the superconformal symmetries, as explained at the end of the previous section.
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