Integrable Gross-Neveu models with fermion-fermion and fermion-antifermion pairing

TL;DR

This paper explores the preservation of integrability in 1+1 dimensional Gross-Neveu models when incorporating fermion-fermion pairing interactions, constructing new exactly solvable models relevant to color superconductivity.

Contribution

It introduces and solves three new integrable models with Cooper pairing and proposes a candidate for a fourth maximally symmetric integrable model.

Findings

Constructed three integrable models with fermion pairing.

Identified a candidate for a maximally symmetric integrable model.

Models serve as toy models for color superconductivity in QCD.

Abstract

The massless Gross-Neveu and chiral Gross-Neveu models are well known examples of integrable quantum field theories in 1+1 dimensions. We address the question whether integrability is preserved if one either replaces the four-fermion interaction in fermion-antifermion channels by a dual interaction in fermion-fermion channels, or if one adds such a dual interaction to an existing integrable model. The relativistic Hartree-Fock-Bogoliubov approach is adequate to deal with the large N limit of such models. In this way, we construct and solve three integrable models with Cooper pairing. We also identify a candidate for a fourth integrable model with maximal kinematic symmetry, the "perfect" Gross-Neveu model. This type of field theories can serve as exactly solvable toy models for color superconductivity in quantum chromodynamics.