4D supersymmetric gauge theories of spacetime translations

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.