Non-perturbative renormalization of the energy momentum tensor in the 2d O(3) nonlinear sigma model

TL;DR

This paper addresses the non-perturbative renormalization of the energy-momentum tensor in the 2D O(3) nonlinear sigma model, using lattice techniques and gradient flow to improve accuracy.

Contribution

It introduces a method employing shifted boundary conditions and gradient flow to accurately determine renormalization constants in the model.

Findings

Precise determination of renormalization constants $z_T$ and $Z_T$.

Use of modified lattice action to reduce discretization artifacts.

Application of gradient flow to define the renormalized coupling.

Abstract

The two-dimensional O(3) nonlinear sigma model is a well known toy model for studying non-perturbative phenomena in quantum field theory. A central challenge is the renormalization of the energy-momentum tensor, which is complicated by the nonlinear realization of the $O(3)$ symmetry leading to non-trivial operator mixing patterns, and by large discretization artifacts affecting the determination of renormalization constants. We present results for the renormalization constants in the non-singlet sector, employing a modified lattice action with shifted boundary conditions and defining the renormalized coupling through the gradient flow. With this we obtain a precise determination of the renormalization constants $z_T$ and $Z_T$