Abstract

A mass parameter for the gauge bosons in gauge-fixed four-dimensional Yang-Mills theory can be accommodated in a local and manifestly BRST-invariant action. The construction is based on the Faddeev-Popov method involving a nonlinear gauge-fixing and a background Nakanishi-Lautrup field. When applied to momentum-dependent masslike deformations, this formalism leads to a full regularization of the theory which explicitly preserves BRST symmetry. We deduce a functional renormalization group equation for the one-particle-irreducible effective action, which has a one-loop form. The master equation is compatible with it, i.e. BRST symmetry is preserved along the flow, and it has a standard regulator-independent Zinn-Justin form. As a first application, we compute the leading-order gluon wave-function renormalization.

Highlights

  • The fact that global symmetries can be implemented exactly is one of the cornerstones of many qualitative and quantitative successes of functional continuum methods in quantum field theory

  • We suggest a novel approach for the construction of renormalization group (RG) flows for gauge systems that relies on Faddeev-Popov quantization and aims at preserving exact BRST symmetry

  • The gauge action Sgf þ Sgh emerging from the Faddeev-Popov construction exhibits an additional globalsymmetry: BRST symmetry

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Summary

INTRODUCTION

The fact that global symmetries can be implemented exactly is one of the cornerstones of many qualitative and quantitative successes of functional continuum methods in quantum field theory. An alternative approach has been developed in [24,25,26,27] introducing a deformed BRST symmetry that includes the regulator and reduces to standard BRST symmetry in the suitable limits This formulation encodes gauge invariance even of the regularized theory in a bilinear master equation but at the same time makes the nonlocality of gauge symmetry in momentum space manifest. Gauge invariance gives rise to a master equation for the (Legendre) effective action which can be brought to standard form with the aid of two additional source fields This facilitates the resolution of the symmetry constraints by conventional algebraic cohomology methods.

CONVENTIONS
QUANTIZATION WITH FOURIER NOISE
MASS AND NONLINEAR GAUGE FIXING
Regularization and nonlinear gauge fixing
Flow of the effective average action
RG FLOW AND THE MASTER EQUATION
RG INITIAL CONDITIONS—THE RECONSTRUCTION PROBLEM
VIII. THE LEADING-ORDER GLUON WAVE-FUNCTION RENORMALIZATION
CONCLUSIONS

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