Solving the ${\mathrm{U}(2)}_L\times {\mathrm{U}(2)}_R$ 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.

Comments: 15 pages, no figure; v2: Typos corrected, Eqs. (48)-(50) corrected, 1 figure added, 1 reference added, 16 pages; v3: minor changes, references added, v4: typos in Eqs. 16,73,111 corrected, computations and results unchanged