4D supersymmetric gauge theories of spacetime translations

TL;DR

This paper investigates the existence and uniqueness of four-dimensional supersymmetric field theories that incorporate local spacetime translations and supersymmetries, revealing a unique class akin to globally supersymmetric Yang-Mills theories.

Contribution

It demonstrates that, under certain conditions, there is a unique class of supersymmetric theories with local spacetime translations and supersymmetries in four dimensions.

Findings

Existence of a unique class of such theories.

These theories have global supersymmetry.

They resemble globally supersymmetric Yang-Mills theories.

Abstract

The paper addresses the question whether in four spacetime dimensions, besides standard supergravity theories, field theories exist whose symmetries include local spacetime translations and supersymmetries generated by transformations whose commutators contain infinitesimal local spacetime translations. It is shown that, up to local field redefinitions, there is a unique class of such supersymmetric field theories satisfying specified prerequisites which particularly concern the field content of the theories. The theories of this class have global supersymmetry and are similar to globally supersymmetric Yang-Mills theories.