Solving the ${\rm U(2)}_L \times {\rm U(2)}_R$ symmetric Nambu--Jona-Lasinio model in 1+1 dimensions

TL;DR

This paper analyzes a variant of the U(2)_L x U(2)_R symmetric Nambu--Jona-Lasinio model in 1+1 dimensions, exploring its vacuum structure, meson spectrum, and phase diagram using semi-classical methods in the large Nc limit.

Contribution

It introduces a detailed study of a less common NJL model with U(2) symmetry in 1+1D, including soliton dynamics and phase behavior, extending semi-classical techniques.

Findings

Determined the vacuum manifold and meson spectrum.

Mapped the phase diagram as a function of temperature and chemical potentials.

Developed a generalized time-dependent Hartree-Fock approach for two flavors.

Abstract

A less well known variant of the Nambu--Jona-Lasinio model with Nc colors and U(2)L X U(2)R chiral symmetry is studied in 1+1 dimensions. Using semi-classical methods appropriate for the large Nc limit, we determine the vacuum manifold, the meson spectrum, massless and massive multi-fermion bound states and the phase diagram as a function of temperature, chemical potential and isospin chemical potential. An important tool to understand soliton dynamics is the generalization of the time-dependent Hartree-Fock approach to two flavors along the lines recently developed by Takahashi in the context of unconventional fermionic superfluids and superconductors.