Renormalisation of the scalar energy-momentum tensor with the Wilson flow

TL;DR

This paper explores the non-perturbative renormalisation of the scalar energy-momentum tensor using Wilson flow in a three-dimensional scalar theory, aiming to facilitate lattice computations of quantum field theories.

Contribution

It extends Wilson flow techniques to scalar theories, providing a framework for non-perturbative renormalisation of the energy-momentum tensor on the lattice.

Findings

Derived renormalisation constants for scalar energy-momentum tensor

Demonstrated the feasibility of Wilson flow in scalar theories

Analyzed translation Ward identities in the context of Wilson flow

Abstract

The non-perturbative computation of the energy-momentum tensor can be used to study the scaling behaviour of strongly coupled quantum field theories. The Wilson flow is an essential tool to find a meaningful formulation of the energy-momentum tensor on the lattice. We extend recent studies of the renormalisation of the energy-momentum tensor in four-dimensional gauge theory to the case of a three-dimensional scalar theory to investigate its intrinsic structure and numerical feasibility on a more basic level. In this paper, we discuss translation Ward identities, introduce the Wilson flow for scalar theory, and present our results for the renormalisation constants of the scalar energy-momentum tensor.