Dynamical chiral symmetry breaking, color superconductivity, and Bose–Einstein condensation in an [formula omitted]-invariant supersymmetric Nambu–Jona-Lasinio model at finite temperature and density

Abstract

We investigate the phenomena of the dynamical chiral symmetry breaking (DCSB), color superconductivity (CSC), and Bose–Einstein condensation (BEC) in a supersymmetric (SUSY) vector-like SU ( N c ) gauge model at finite temperature and density. Both the N = 1 four-dimensional and N = 2 three-dimensional cases are considered. We employ the N = 1 four-dimensional generalized SUSY Nambu–Jona-Lasinio model ( N = 1 generalized SNJL 4 ) with a chemical potential as the model Lagrangian. The N = 2 three-dimensional theory is obtained by a simple dimensional reduction scheme of the four-dimensional counterpart. In order to realize the DCSB and BCS-type CSC in this model, we introduce a SUSY soft mass term. After adopting the method of SUSY auxiliary fields with the Fierz transformation in color and flavor spaces, we discuss several possible breaking schemes of the global symmetries of the model. The integrations of the auxiliary fields of composites in the effective potential are performed by using the steepest descent approximation. Under the finite-temperature Matsubara formalism, the gap equations are derived and solved. The roles of both the boson and fermion sectors in the BEC, DCSB and CSC are examined by the quasiparticle excitation spectra and the gap equations. The physical properties of the DCSB and the CSC are studied in detail. Examination on the physical property of the BEC is beyond scope of this paper. It is found that the BEC, DCSB and CSC can coexist under a condition of model parameters. Several important observations are obtained in the method of the construction of the SUSY BCS-type theory, starting from a SUSY field theoretical framework.