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
Summary
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.
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