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

## TL;DR

This paper constructs the $ ext{N}=3$ Weyl multiplet in four dimensions, providing foundational transformations essential for developing superconformal calculus in $ ext{N}=3$, $D=4$ supergravity theories.

## Contribution

It introduces the $ ext{N}=3$ Weyl multiplet by truncating from $ ext{N}=4$, coupling with a current multiplet, and implementing a nonlinear soft algebra extension.

## Key findings

- First explicit $ ext{N}=3$ Weyl multiplet construction
- Extension of superconformal algebra to nonlinear level
- Foundation for $ ext{N}=3$ superconformal calculus

## 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 $\mathcal{N}=3$, $D = 4$.