The $\mathcal{N}=3$ Weyl Multiplet in Four Dimensions

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 su$(2,2|3)$. This is the first step towards a superconformal calculus for $\mathcal{N}=3$, $D=4$.

43 pages, v2: completely revised version; v3: minor fixes; v4: minor fixes, version to be published in JHEP