A Detailed Investigation of First and Second Order Supersymmetries for Off-Shell N = 2 and N = 4 Supermultiplets

TL;DR

This paper explores the intricate supersymmetry structures of N=2 and N=4 supermultiplets in four-dimensional super-Yang Mills theories, focusing on first and second order supersymmetries and their implications for auxiliary field closure.

Contribution

It provides a detailed analysis of first and second order supersymmetries in off-shell N=2 and N=4 supermultiplets, revealing new symmetry structures and potential solutions to auxiliary field closure issues.

Findings

Identified additional symmetries from central charges.

Calculated second order supersymmetries.

Suggested pathways to auxiliary field closure without infinite fields.

Abstract

This paper investigates the d = 4, N = 4 Abelian, global Super-Yang Mills system (SUSY-YM). It is shown how the N = 2 Fayet Hypermultiplet (FH) and N = 2 vector multiplet (VM) are embedded within. The central charges provide a plethora of information as to further symmetries of the Lagrangian. Several of these symmetries are calculated to second order. It is hoped that investigations such as these may yield avenues to help solve the auxiliary field closure problem for d = 4, N = 4, SUSY-YM and the d = 4, N = 2 Fayet-Hypermultiplet, without using an infinite number of auxiliary fields.