TY - JOUR
T1 - Gradient flow exact renormalization group
T2 - Inclusion of fermion fields
AU - Miyakawa, Yuki
AU - Suzuki, Hiroshi
N1 - Publisher Copyright:
© 2021 The Author(s). Published by Oxford University Press on behalf of the Physical Society of Japan.
PY - 2021/8/1
Y1 - 2021/8/1
N2 - 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 $D=2$.
AB - 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 $D=2$.
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U2 - 10.1093/ptep/ptab100
DO - 10.1093/ptep/ptab100
M3 - Article
AN - SCOPUS:85114750755
VL - 2021
JO - Progress of Theoretical and Experimental Physics
JF - Progress of Theoretical and Experimental Physics
SN - 2050-3911
IS - 8
M1 - 083B04
ER -