BRS symmetry from renormalization group flow

TL;DR

This paper demonstrates how the Slavnov-Taylor identities in SU(2) Yang-Mills theory can be proven perturbatively using the exact renormalization group, highlighting the roles of locality and solvability.

Contribution

It provides a perturbative proof of the Slavnov-Taylor identities within the exact renormalization group framework for SU(2) Yang-Mills theory, emphasizing locality and solvability.

Findings

Proof of ST identities via RG flow in SU(2) Yang-Mills

Identification of locality and solvability as key properties

Perturbative validation of gauge symmetry constraints

Abstract

By using the exact renormalization group formulation we prove perturbatively the Slavnov-Taylor (ST) identities in SU(2) Yang-Mills theory. This results from two properties: {\it locality}, i.e. the ST identities are valid if their local part is valid; {\it solvability}, i.e. the local part of ST identities is valid if the couplings of the effective action with non-negative dimensions are properly chosen.