Energy-momentum tensor from the Yang-Mills gradient flow

TL;DR

This paper derives a formula connecting the small flow-time behavior of gauge-invariant products in Yang-Mills theory to the properly normalized energy-momentum tensor, enabling lattice computations of its correlation functions.

Contribution

It introduces a new formula linking flow-time expansions to the energy-momentum tensor, facilitating nonperturbative calculations in lattice gauge theory.

Findings

Derived a formula relating flow-time behavior to the energy-momentum tensor.

Provides a method for lattice simulations to compute energy-momentum tensor correlations.

Ensures local products are regularization-independent and renormalizable.

Abstract

The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can furthermore be expanded by renormalized local operators at zero flow time with finite coefficients that are governed by renormalization group equations. Using these facts, we derive a formula that relates the small flow-time behavior of certain gauge-invariant local products and the correctly-normalized conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides a possible method to compute the correlation functions of a well-defined energy-momentum tensor by using lattice regularization and Monte Carlo simulation.