Lattice energy-momentum tensor with Symanzik improved actions

TL;DR

This paper constructs a lattice energy-momentum tensor for Symanzik improved actions in scalar models, ensuring correct quantum anomalies and enabling applications in Monte Carlo simulations.

Contribution

It introduces a method to define the energy-momentum tensor on the lattice for Symanzik improved actions using Ward identities and matching procedures.

Findings

Operators reproduce the correct one-loop scale anomaly.

Applicable to Monte Carlo simulations of sigma models.

Provides a consistent lattice formulation of energy-momentum tensor.

Abstract

We define the energy-momentum tensor on lattice for the $\lambda \phi^4$ and for the nonlinear $\sigma$-model Symanzik tree-improved actions, using Ward identities or an explicit matching procedure. The resulting operators give the correct one loop scale anomaly, and in the case of the sigma model they can have applications in Monte Carlo simulations.