Note on "Equivalence Between Different Auxiliary Field Formulations of ${\cal N}=1$ Supergravity Coupled to Matter"

TL;DR

This paper clarifies a correction to a previous claim that different auxiliary field formulations of 4D ${ m N}=1$ supergravity could be unified via a U(1) gauge symmetry, emphasizing the importance of accuracy in theoretical physics.

Contribution

The paper provides a correction to earlier work, refining the understanding of auxiliary field formulations in 4D ${ m N}=1$ supergravity and their relation to U(1) gauge symmetry.

Findings

The original unification claim was incorrect.

A critical error was identified in the previous formulation.

The correction clarifies the limitations of auxiliary field equivalences.

Abstract

In the version 1 of this paper, we claimed that 4D ${\cal N}=1$ supergravity formulations with different auxiliary fields can be unified using U(1) gauge symmetry, whose gauge superfield does not have a kinetic term. However, after submission, we found a critical error in our statement. This is the note on the paper of the version 1.