Fixed Point Structure of Gradient Flow Exact Renormalization Group for Scalar Field Theories

Abstract

Gradient Flow Exact Renormalization Group (GFERG) is a framework to define the Wilson action via a gradient flow equation. We study the fixed point structure of the GFERG equation associated with a general gradient flow equation for scalar field theories and show that it is the same as that of the conventional Wilson-Polchinski (WP) equation in general. Furthermore, we discuss that the GFERG equation has a similar RG flow structure around a fixed point to the WP equation. We illustrate these results with the $O(N)$ non-linear sigma model in $4-\epsilon$ dimensions and the Wilson-Fisher fixed point.

arXiv comment23 pages, 1 figure

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Cited by in corpus (6)

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• Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
• A basis of the gradient flow exact renormalization group for gauge theory
• Two-loop gradient-flow renormalization of scalar QCD
• Functional Renormalization Group Analysis of $O(3)$ Nonlinear Sigma Model and Non-Abelian Bosonization Duality
• Perturbative analysis of the Wess-Zumino flow