A chargeless complex vector matter field in supersymmetric scenario

TL;DR

This paper develops a supersymmetric model for a chargeless complex vector matter field by combining scalar superfields, deriving equations of motion, and ensuring consistent symmetry and degrees of freedom, laying groundwork for future extensions.

Contribution

It introduces a novel supersymmetric formulation of a chargeless complex vector field using scalar superfields, ensuring symmetry and consistency in the model.

Findings

Derived equations of motion of Proca type fields

Confirmed the mass equality of fields on-shell

Established a framework for supersymmetric charged vector fields

Abstract

In this paper we construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two no-chiral scalar superfields in order to take the vector component field to build the chargeless complex vector superpartner where the respective field strength transforms as matter fields by a global $U(1)$ gauge symmetry. To the aim to deal with consistent terms without breaking the global $U(1)$ symmetry it imposes a choice to the complex combination revealing a kind of symmetry between the choices and eliminate the extra degrees of freedom consistently with the supersymmetry. As the usual case the mass supersymmetric sector contributes as a complement to dynamics of the model. We obtain the equations of motion of the Proca's type field, for the chiral spinor fields and for the scalar field on the mass-shell which show the same mass as expected. This work establishes the firsts steps to extend the analysis of charged massive vector field in a supersymmetric scenario.