Stochastic Renormalization Group and Gradient Flow in Scalar Field Theory

TL;DR

This paper establishes a theoretical connection between gradient flow and the functional renormalization group using stochastic processes, providing new tools for analyzing scalar field theories through lattice simulations.

Contribution

It introduces a novel stochastic framework linking gradient flow to FRG, enabling numerical measurement of anomalous dimensions in lattice scalar field theories.

Findings

Derived correlator scaling formulas applicable in lattice simulations

Preliminary measurements of anomalous dimensions in 3D ^4 theory

Established a stochastic representation of FRG observables

Abstract

Recently, the connections between gradient flow and renormalization group have been explored analytically and numerically. Gradient flow (when modified by a field rescaling) can be characterized as a continuous blocking transformation. In this work, we draw a connection between gradient flow and functional renormalization group by describing how FRG can be represented by a stochastic process, and how the stochastic observables relate to gradient flow observables. The relation implies correlator scaling formulae that can be applied numerically in lattice simulations. We present preliminary results on anomalous dimensions obtained from such measurements in the context of 3-dimensional lattice $\phi^4$ theory.