Feynman Rules in N=2 projective superspace III: Yang-Mills multiplet

TL;DR

This paper develops Feynman rules for N=2 supersymmetric Yang-Mills theory in projective superspace, simplifying gauge fixing and propagator derivation, and matching N=1 component results, thus advancing computational tools for N=2 supersymmetric models.

Contribution

It introduces a method to derive Feynman rules directly in N=2 projective superspace, including gauge fixing and propagator calculations, bridging N=2 and N=1 formalisms.

Findings

Derived N=2 superspace Feynman rules for Yang-Mills and hypermultiplets.

Simplified gauge fixing leads to invertible kinetic terms.

Matched N=1 component propagators with known results.

Abstract

The kinetic action of the N=2 Yang-Mills vector multiplet can be written in projective N=2 superspace using projective multiplets. It is possible to perform a simple N=2 gauge fixing, which translated to N=1 component language makes the kinetic terms of gauge potentials invertible. After coupling the Yang-Mills multiplet to unconstrained sources it is very simple to integrate out the gauge fixed vector multiplet from the path integral of the free theory and obtain the N=2 propagator. Its reduction to N=1 components agrees with the propagators of the gauge fixed N=1 component superfields. The coupling of Yang-Mills multiplets and hypermultiplets in N=2 projective superspace allows us to define Feynman rules in N=2 superspace for these two fields.