Gradient flow exact renormalization group -- inclusion of fermion fields

Abstract

The gradient flow exact renormalization group (GFERG) is an exact renormalization group motivated by the Yang--Mills gradient flow and its salient feature is a manifest gauge invariance. We generalize this GFERG, originally formulated for the pure Yang--Mills theory, to vector-like gauge theories containing fermion fields, keeping the manifest gauge invariance. For the chiral symmetry we have two options: one possible formulation preserves the conventional form of the chiral symmetry and the other simpler formulation realizes the chiral symmetry in a modified form à la Ginsparg--Wilson. We work out a gauge-invariant local Wilson action in quantum electrodynamics to the lowest nontrivial order of perturbation theory. This Wilson action reproduces the correct axial anomaly in~$D=2$.

arXiv comment23 pages, the final version to appear in PTEP

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Cited by in corpus (6)

• Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
• Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
• A basis of the gradient flow exact renormalization group for gauge theory
• Higher derivative extension of the functional renormalization group
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Perturbative analysis of the Wess-Zumino flow