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.

23 pages, 1 figure

References in corpus (10)

• Exact evolution equation for the effective potential
• Perturbative analysis of the gradient flow in non-abelian gauge theories
• Chiral symmetry breaking in continuum QCD
• The phase structure of the Polyakov--quark-meson model beyond mean field
• Chiral phase boundary of QCD at finite temperature
• Ising exponents from the functional renormalisation group
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Gradient Flow of O(N) nonlinear sigma model at large N
• Gradient flow exact renormalization group
• Renormalization group and diffusion equation