Cubic supersymmetry and abelian gauge invariance

TL;DR

This paper explores an extended form of supersymmetry called cubic supersymmetry, focusing on bosonic multiplets with higher-form gauge fields, their invariant Lagrangians, and the relationship with U(1) gauge invariance, highlighting gauge-fixing and lack of self-interactions.

Contribution

It introduces invariant free Lagrangians involving 2-, 3-, and 4-form fields within cubic supersymmetry and analyzes their interaction with U(1) gauge symmetry, including gauge-fixing implications.

Findings

Constructed invariant free Lagrangians with higher-form fields

Analyzed the interplay between cubic supersymmetry and U(1) gauge invariance

Identified the automatic gauge-fixing and absence of self-interaction terms

Abstract

On the basis of recent results extending non-trivially the Poincar\'e symmetry, we investigate the properties of bosonic multiplets including $2-$form gauge fields. Invariant free Lagrangians are explicitly built which involve possibly $3-$ and $4-$form fields. We also study in detail the interplay between this symmetry and a U(1) gauge symmetry, and in particular the implications of the automatic gauge-fixing of the latter associated to a residual gauge invariance, as well as the absence of self-interaction terms.