Renormalization Group Properties of Scalar Field Theory Using Gradient Flow

TL;DR

This paper explores the use of gradient flow to define and analyze renormalization group transformations in scalar field theory, providing a novel approach to studying critical phenomena and fixed points.

Contribution

It introduces a new formulation of RG transformations for scalar fields using gradient flow and presents preliminary numerical results for critical exponents at the Wilson-Fisher fixed point.

Findings

Gradient flow suppresses high-modes of the field.

Preliminary numerical results for critical exponents.

Potential for new analytical and numerical RG methods.

Abstract

Gradient flow has proved useful in the definition and measurement of renormalized quantities on the lattice. Recently, the fact that it suppresses high-modes of the field has been used to construct new, continuous RG transformations both analytically and on the lattice, distinct from the usual blocking techniques in spin models and gauge theories. In this work, we discuss such a formulation for scalar field theory, and we present preliminary numerical results for its application to the determination of critical exponents at the Wilson-Fisher fixed point of three-dimensional $\phi^4$ theory.