WT identities for proper vertices and renormalization in a superspace formulation of gauge theories

TL;DR

This paper presents a superspace formulation of gauge theories that simplifies the Ward-Takahashi identities for proper vertices, facilitating the understanding of superfield renormalizations and symmetry properties in Yang-Mills theories.

Contribution

It introduces a compact WT identity in superspace and demonstrates its role in clarifying superfield renormalizations and symmetries in gauge theories.

Findings

WT identity expressed as ∂Γ/∂θ=0 in superspace

Superfield multiplet renormalizations explained

Symmetries of Yang-Mills theory renormalization clarified

Abstract

We formulate the WT identity for proper vertices in a simple and compact form $\partial \Gamma / {\partial \theta } =0 $ in a superspace formulation of gauge theories proposed earlier. We show this WT identity (together with a subsidiary constraint) lead, in transparent way, the superfield superspace multiplet renormalizations formulated earlier (and shown to explain symmetries of Yang-Mills theory renormalization).