Renormalization of the energy-momentum tensor in three-dimensional scalar $SU(N)$ theories using the Wilson flow

TL;DR

This paper develops a nonperturbative method using Wilson flow to renormalize the energy-momentum tensor in three-dimensional scalar SU(N) theories, addressing divergences and operator mixing.

Contribution

It introduces a Wilson flow-based procedure for renormalizing the energy-momentum tensor in 3D scalar SU(N) theories, including mixing coefficient calculations.

Findings

Numerical results for the mixing coefficient in N=2 theory.

Demonstration of Wilson flow's effectiveness in eliminating divergences.

Validation of the renormalization procedure on the lattice.

Abstract

A nonperturbative determination of the energy-momentum tensor is essential for understanding the physics of strongly coupled systems. The ability of the Wilson flow to eliminate divergent contact terms makes it a practical method for renormalizing the energy-momentum tensor on the lattice. In this paper, we utilize the Wilson flow to define a procedure to renormalize the energy-momentum tensor for a three-dimensional massless scalar field in the adjoint of $SU(N)$ with a $\varphi^4$ interaction on the lattice. In this theory the energy-momentum tensor can mix with $\varphi^2$ and we present numerical results for the mixing coefficient for the $N=2$ theory.