Duality between quark-quark and quark-antiquark pairing in 1+1 dimensional large N models

TL;DR

This paper reveals a duality in 1+1 dimensional large N models, showing that chiral symmetry breaking and superconductivity are two descriptions of the same physics through a canonical transformation.

Contribution

It introduces a canonical transformation that maps the chiral Gross-Neveu model onto a Cooper pair model, interchanging baryon number and axial charge.

Findings

Chiral symmetry breaking and superconductivity are dual descriptions.

The same physics can be viewed as quark-antiquark or quark-quark pairing.

A canonical transformation links these two models.

Abstract

We identify a canonical transformation which maps the chiral Gross-Neveu model onto a recently proposed Cooper pair model. Baryon number and axial charge are interchanged. The same physics can be described either as chiral symmetry breaking (quark-antiquark pairing) or as superconductivity (quark-quark pairing).