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

TL;DR

This paper investigates the fixed point structure of the Gradient Flow Exact Renormalization Group (GFERG) for scalar field theories, showing its equivalence to the Wilson-Polchinski equation and analyzing flow behavior near fixed points.

Contribution

It demonstrates that GFERG shares the same fixed point structure as the Wilson-Polchinski equation for scalar theories, providing insights into RG flow similarities.

Findings

GFERG fixed points match Wilson-Polchinski fixed points

RG flow structures are similar near fixed points

Illustrated with $O(N)$ sigma model and Wilson-Fisher fixed point

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.