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

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.