Energy-momentum tensor on the lattice: non-perturbative renormalization in Yang--Mills theory

TL;DR

This paper develops a non-perturbative method to construct and renormalize the energy-momentum tensor on the lattice in SU(3) Yang--Mills theory, ensuring it satisfies Ward identities and reproduces the continuum trace anomaly.

Contribution

It introduces a lattice construction of the energy-momentum tensor that obeys Ward identities and determines its renormalization constants with high precision using numerical simulations.

Findings

Renormalization constants determined with ~0.5% accuracy

Method applicable to SU(3) Yang--Mills with Wilson action

Ensures tensor satisfies Ward identities and trace anomaly

Abstract

We construct an energy-momentum tensor on the lattice which satisfies the appropriate Ward Identities (WIs) and has the right trace anomaly in the continuum limit. It is defined by imposing suitable WIs associated to the Poincare` invariance of the continuum theory. These relations come forth when the length of the box in the temporal direction is finite, and they take a particularly simple form if the coordinate and the periodicity axes are not aligned. We implement the method for the SU(3) Yang--Mills theory discretized with the standard Wilson action in presence of shifted boundary conditions in the (short) temporal direction. By carrying out extensive numerical simulations, the renormalization constants of the traceless components of the tensor are determined with a precision of roughly half a percent for values of the bare coupling constant in the range 0<= g^2_0<=1.