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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.

The $$ \mathcal{N} $$ = 3 Weyl multiplet in four dimensions