Renormalization group improvement of the effective potential in a (1+1) dimensional Gross-Neveu model

TL;DR

This paper applies renormalization group techniques to improve the effective potential calculation in a (1+1) dimensional Gross-Neveu model, revealing insights into dynamical symmetry breaking and mass generation.

Contribution

It introduces an improved effective potential using RGE and leading logs approximation up to six loops, enhancing previous perturbative results for the GN model.

Findings

Demonstrates dimensional transmutation in the model.

Shows improved potential affects symmetry breaking analysis.

Provides comparison between improved and unimproved potentials.

Abstract

In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective potential and the study of Dynamical Symmetry Breaking (DSB) in an Gross-Neveu (GN) model with N fermions fields in (1+1) dimensional space-time, which can be applied as a model to describe certain properties of the polyacetylene. The classical Lagrangian of the model is scale invariant, but radiative corrections to the effective potential can lead to dimensional transmutation, when a dimensionless parameter (coupling constant) of the classical Lagrangian is exchanged for a dimensionful one, a dynamically generated mass for the fermion fields. For the model we are considering, perturbative calculations of the effective potential and renormalization group functions up to three loops are available, but we use the RGE and the leading logs approximation to calculate an improved effective potential, including contributions up to six loops orders. We then perform a systematic study of the general aspects of DSB in the GN model with finite N, comparing the results we obtain with the ones derived from the original unimproved effective potential we started with.