A basis of the gradient flow exact renormalization group for gauge theory
arXiv:2506.23567 · doi:10.1093/ptep/ptaf115
Abstract
The gradient flow exact renormalization group (GFERG) is a variant of the exact renormalization group (ERG) for gauge theory that is aimed at preserve gauge invariance as manifestly as possible. It achieves this goal by utilizing the Yang--Mills gradient flow or diffusion for the block-spin process. In this paper, we formulate GFERG by the Reuter equation in which the block spinning is done by Gaussian integration. This formulation provides a simple understanding of various points of GFERG, unresolved thus far. First, there exists a unique ordering of functional derivatives in the GFERG equation that remove ambiguity of contact terms. Second, perturbation theory of GFERG suffers from unconventional ultraviolet (UV) divergences if no gauge fixing is introduced. This explains the origin of some UV divergences we have encountered in perturbative solutions to GFERG. Third, the modified correlation functions calculated with the Wilson action in GFERG coincide with the correlation functions of diffused or flowed fields calculated with the bare action. This shows the existence of a Wilson action that reproduces precisely the physical quantities computed by the gradient flow formalism (up to contact terms). We obtain a definite ERG interpretation of the gradient flow. The formulation given in this paper provides a basis for further perturbative/nonperturbative computations in GFERG, preserving gauge invariance maximally.
arXiv comment27 pages, the final version to appear in PTEP
References in corpus (32)
- Exact evolution equation for the effective potential
- The Exact Renormalisation Group and Approximate Solutions
- Aspects of the Functional Renormalisation Group
- Properties and uses of the Wilson flow in lattice QCD
- The nonperturbative functional renormalization group and its applications
- Perturbative analysis of the gradient flow in non-abelian gauge theories
- Infinite N phase transitions in continuum Wilson loop operators
- Fundamentals of the Exact Renormalization Group
- Chiral symmetry and the Yang--Mills gradient flow
- A gauge invariant exact renormalization group I
- Realization of symmetry in the ERG approach to quantum field theory
- A Generalised Manifestly Gauge Invariant Exact Renormalisation Group for SU(N) Yang-Mills
- A gauge invariant exact renormalization group II
- Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
- A Manifestly Gauge Invariant, Continuum Calculation of the SU(N) Yang-Mills two-loop beta function
- Analytical approximation schemes for solving exact renormalization group equations. II Conformal mappings
- Proof of the renormalizability of the gradient flow
- Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
- Derivation of a Gradient Flow from ERG
- Equivalence of Wilson Actions
- Stochastic Renormalization Group and Gradient Flow
- Gradient flow exact renormalization group
- Cooling Stochastic Quantization with colored noise
- Renormalization group and diffusion equation
- The Yang-Mills gradient flow and lattice effective action
- Gradient flow exact renormalization group -- inclusion of fermion fields
- Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories
- Supersymmetric gradient flow in the Wess-Zumino model
- Chiral anomaly as a composite operator in the gradient flow exact renormalization group formalism
- Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
- Supersymmetric gradient flow in 4d N=1 SQCD
- Perturbative analysis of the Wess-Zumino flow