Space-time symmetries and the Yang-Mills gradient flow

TL;DR

This paper explores how the gradient flow technique can be used to analyze space-time symmetries in gauge theories, leading to nonperturbative renormalization methods and insights into scale invariance on the lattice.

Contribution

It introduces a novel approach to study space-time symmetries via the gradient flow, including Ward identities and nonperturbative renormalization of the energy-momentum tensor.

Findings

Derivation of Ward identities for gauge theories with gradient flow

Nonperturbative renormalization of the energy-momentum tensor on the lattice

Application to dilatations and scale invariance studies

Abstract

The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.