Universal formula for the energy--momentum tensor via a flow equation in the Gross--Neveu model

TL;DR

This paper introduces a flow equation in the two-dimensional Gross--Neveu model to validate a universal formula for the energy--momentum tensor, confirming its correctness through $1/N$ expansion and thermodynamic consistency.

Contribution

It demonstrates the validity of a universal energy--momentum tensor formula using a flow equation and $1/N$ expansion in the Gross--Neveu model, supporting similar approaches in lattice gauge theory.

Findings

The formula reproduces correct normalization and conservation law.

The expectation value at finite temperature matches thermodynamic quantities.

Supports the use of flow-based constructions for energy--momentum tensors in lattice theories.

Abstract

For the fermion field in the two-dimensional Gross--Neveu model, we introduce a flow equation that allows a simple $1/N$ expansion. By employing the $1/N$ expansion, we examine the validity of a universal formula for the energy--momentum tensor which is based on the small flow-time expansion. We confirm that the formula reproduces a correct normalization and the conservation law of the energy--momentum tensor by computing the translation Ward--Takahashi relation in the leading non-trivial order in the $1/N$ expansion. Also, we confirm that the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy--momentum tensor via the gradient/Wilson flow in lattice gauge theory.