Off--shell formulation of N = 2 Super Yang--Mills theories coupled to matter without auxiliary fields

TL;DR

This paper develops an off-shell formulation for N=2 Super Yang--Mills theories with matter, avoiding auxiliary fields by using a nilpotent operator that consolidates all symmetries, simplifying the algebraic structure.

Contribution

It introduces a novel method to formulate N=2 Super Yang--Mills theories off-shell without auxiliary fields by employing a nilpotent operator that unifies all symmetries.

Findings

Unified nilpotent operator for all symmetries

Simplification of algebraic structure of the theory

Avoidance of auxiliary fields in off-shell formulation

Abstract

N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge transformations and equations of motion. The difficulties hidden in such an algebraic structure are well known: almost always auxiliary fields can be introduced in order to put the formalism off--shell, but still the field dependent gauge transformations give rise to an infinite dimensional algebra quite hard to deal with. However, it is possible to avoid all these problems by collecting into an unique nilpotent operator all the symmetries defining the theory, namely ordinary BRS, supersymmetries and translations. According to this method the role of the auxiliary fields is covered by the external sources coupled, as usual, to the nonlinear variations of the quantum fields. The analysis is then formally reduced to that of ordinary Yang--Mills theory.