Field Representations of Vector Supersymmetry

TL;DR

This paper explores various field representations of vector supersymmetry with different superspins and central charges, introducing new multiplets, actions, and superspace formalisms, and analyzing their properties in Euclidean and Minkowski spacetimes.

Contribution

It presents novel multiplets for vector supersymmetry with nonvanishing central charges, develops a superspace formalism, and compares representations in Euclidean and Minkowski spacetimes.

Findings

Two multiplets for Y=0 with different central charge actions

A multiplet for Y=1/2 involving scalar, vector, and two-form fields

Development of a superspace formalism for vector supersymmetry

Abstract

We study some field representations of vector supersymmetry with superspin Y=0 and Y=1/2 and nonvanishing central charges. For Y=0, we present two multiplets composed of four spinor fields, two even and two odd, and we provide a free action for them. The main differences between these two multiplets are the way the central charge operators act and the compatibility with the Majorana reality condition on the spinors. One of the two is related to a previously studied spinning particle model. For Y=1/2, we present a multiplet composed of one even scalar, one odd vector and one even selfdual two-form, which is a truncation of a known representation of the tensor supersymmetry algebra in Euclidean spacetime. We discuss its rotation to Minkowski spacetime and provide a set of dynamical equations for it, which are however not derived from a Lagrangian. We develop a superspace formalism for vector supersymmetry with central charges and we derive our multiplets by superspace techniques. Finally, we discuss some representations with vanishing central charges.