Baryons in Massive Gross-Neveu Models

TL;DR

This paper extends the understanding of baryons in (1+1)-dimensional Gross-Neveu models by incorporating explicit symmetry breaking, providing exact solutions and effective theories for both discrete and continuous chiral symmetries.

Contribution

It generalizes baryon solutions to models with explicit symmetry breaking, deriving exact solutions for discrete symmetry and effective theories with systematic corrections for continuous symmetry.

Findings

Exact solutions for baryons with arbitrary bare mass in discrete symmetry models.

Re-derivation of a Skyrme-type model for continuous symmetry cases.

Systematic computation of corrections to the sine-Gordon effective theory.

Abstract

Baryons in the large N limit of (1+1)-dimensional Gross-Neveu models with either discrete or continuous chiral symmetry have long been known. We generalize their construction to the case where the symmetry is explicitly broken by a bare mass term in the Lagrangian. In the discrete symmetry case, the exact solution is found for arbitrary bare fermion mass, using the Hartree-Fock approach. It is mathematically closely related to polarons and bipolarons in conducting polymers. In the continuous symmetry case, a derivative expansion allows us to rederive a formerly proposed Skyrme-type model and to compute systematically corrections to the leading order description based on an effective sine-Gordon theory.