Comment on "The N = 3 Weyl Multiplet in Four Dimensions"

TL;DR

This paper critically examines the previously constructed N=3 Weyl multiplet in four dimensions, identifies inconsistencies in earlier transformation rules, and proposes a new, consistent approach to derive the transformation rules and soft algebra.

Contribution

It introduces a novel method to compute the N=3 Weyl multiplet's transformation rules ensuring internal consistency, correcting prior inaccuracies.

Findings

Identified inconsistencies in previous transformation rules.

Developed a new consistent approach for deriving the multiplet's transformations.

Provided corrected soft algebra for the N=3 Weyl multiplet.

Abstract

N = 3 Weyl multiplet in four dimensions was first constructed in J van Muiden et al (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the nonlinear variations using the superconformal algebra. The multiplet of currents was obtained by a truncation of the multiplet of currents for the N = 4 vector multiplet. While the procedure seems to be correct, the result suffers from several inconsistencies. The inconsistencies are observed in the transformation rules as well as the field dependent structure constants in the corresponding soft algebra. We take a different approach, and compute the transformation rule as well as the corresponding soft algebra by demanding consistency.