Supersymmetric construction of self-consistent condensates in large N GN model: solitons on finite-gap potentials

TL;DR

This paper explores a supersymmetric framework to construct self-consistent condensates in the large N Gross-Neveu model, revealing hidden symmetries and their relation to integrable hierarchies and soliton solutions.

Contribution

It introduces a supersymmetric approach to extend stationary solutions of the Gross-Neveu model using Darboux-Miura transformations and integrable hierarchies.

Findings

Identification of hidden supersymmetry in the Gross-Neveu model.

Connection between superpotentials and self-consistent condensates.

Extension of stationary solutions via Darboux transformations.

Abstract

In the present work, the set of stationary solutions of the Gross-Neveu model in 't Hooft limit is extended. Such extension is obtained by striving a hidden supersymmetry associated to disconnected sets of stationary solutions. How the supersymmetry arises from the Darboux-Miura transformations between Lax pairs of the stationary modified Korteweg-de Vries and the stationary Korteweg-de Vries hierarchies is shown, associating the correspondent superpotentials to self-consistent condensates for the Gross-Neveu model.