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

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.