The three-dimensional non-anticommutative superspace

TL;DR

This paper introduces two formulations of a three-dimensional non-anticommutative superspace with Clifford relations, constructs supersymmetry generators, and develops a scalar superfield theory including propagator calculation and interaction prescription.

Contribution

It presents novel formulations of non-anticommutative superspace in three dimensions and develops the associated superfield theory with interaction methods.

Findings

Constructed supersymmetry generators satisfying standard relations.

Formulated a scalar superfield theory in the new superspace.

Calculated the propagator and proposed interaction methods.

Abstract

We propose two alternative formulations for a three-dimensional non-anticommutative superspace in which some of the fermionic coordinates obey Clifford anticommutation relations. For this superspace, we construct the supersymmetry generators satisfying standard anticommutation relations and the corresponding supercovariant derivatives. We formulate a scalar superfield theory in such a superspace and calculate its propagator. We also suggest a prescription for the introduction of interactions in such theories.