Kink dynamics, sinh-Gordon solitons and strings in AdS(3) from the Gross-Neveu model

TL;DR

This paper reveals a deep connection between quantum fermions, classical sinh-Gordon solitons, and strings in AdS(3), demonstrating the full solvability of the N-kink-antikink problem in the Gross-Neveu model.

Contribution

It establishes a quantitative relationship linking fermions, sinh-Gordon solitons, and classical strings in AdS(3), highlighting the model's integrability.

Findings

Demonstrates a relationship between fermions, solitons, and strings.

Shows the full solvability of the N-kink-antikink problem.

Provides insights into quantum-classical correspondence.

Abstract

Guided by a study of kink-antikink scattering in the Gross-Neveu model and other known solutions of the Hartree-Fock approach of a particularly simple type, we demonstrate a quantitative relationship between three different problems: Quantized 1+1-dimensional fermions in the large N limit, solitons of the classical sinh-Gordon equation and classical strings moving in 3-dimensional anti de Sitter space. Aside from throwing light on the relationship between quantum field theory and classical physics, this points to the full solvability of the dynamical N-kink-antikink problem in the Gross-Neveu model.