BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group

TL;DR

This paper extends the realization of BRS symmetry within the Wilsonian renormalization group framework to general gauge theories, revealing a deep structure via antifield formalism and connecting the quantum master equation with RG flow and Ward-Takahashi identities.

Contribution

It demonstrates that the effective BRS symmetry can be formulated for general gauge theories using antifield formalism, linking the quantum master equation with RG flow and Ward-Takahashi identities.

Findings

The average action obeys the quantum master equation if the UV action does.

RG flow is generated by canonical transformations in field-antifield space.

The quantum master equation remains valid as regularization is removed.

Abstract

Recently we made a proposal for realization of an effective BRS symmetry along the Wilsonian renormalization group flow. In this paper we show that the idea can be naturally extended for the most general gauge theories. Extensive use of the antifield formalism is made to reveal some remarkable structure of the effective BRS symmetry. The average action defined with a continuum analog of the block spin transformation obeys the quantum master equation (QME), provided that an UV action does so. We show that the RG flow described by the exact flow equations is generated by canonical transformations in the field-antifield space. Using the relation between the average action and the Legendre effective action, we establish the equivalence between the QME for the average action and the modified Ward-Takahashi identity for the Legendre action. The QME remains intact when the regularization is removed.