Twodimensional model with chiral condensates and Cooper pairs having a QCDlike phase structure
Abstract
We generalize our previous model to an O(N) symmetric twodimensional model which possesses chiral symmetry breaking (<ψ¯ψ> condensate) and superconducting (Cooper pair <ψψ> condensates) phases at large N. At zero temperature and density, the model can be solved analytically in the largeN limit. We perform the renormalization explicitly and obtain a closed form expression of the effective potential. There exists a renormalization group invariant parameter δ that determines which of the <ψ¯ψ> (δ>0) or <ψψ> (δ<0) condensates exist in the vacuum. At finite temperatures and densities, we map out the phase structure of the model by a detailed numerical analysis of the renormalized effective potential. For δ positive and sufficiently large, the phase diagram in the μT (chemical potentialtemperature) plane exactly mimics the features expected for QCD with two light flavors of quarks. At low temperatures there exists lowμ chiral symmetry breaking and highμ Cooper pair condensate regions which are separated by a firstorder phase transition. At high μ, when the temperature is raised, the system undergoes a secondorder phase transition from the superconducting phase to an unbroken phase in which both condensates vanish. For a range of values of δ the theory possesses a tricritical point (μ_{tc} and T_{tc}); for μ>μ_{tc} (μ<μ_{tc}) the phase transition from the low temperature chiral symmetry breaking phase to unbroken phase is first order (second order). For the range of δ in which the system mimics QCD, we expect the model to be useful for the investigation of dynamical aspects of nonequilibrium phase transitions, and to provide information relevant to the study of relativistic heavy ion collisions and the dense interiors of neutron stars.
 Publication:

Physical Review D
 Pub Date:
 February 2000
 DOI:
 10.1103/PhysRevD.61.045011
 arXiv:
 arXiv:hepph/9909296
 Bibcode:
 2000PhRvD..61d5011C
 Keywords:

 11.30.Qc;
 11.10.Kk;
 11.10.Wx;
 11.15.Pg;
 Spontaneous and radiative symmetry breaking;
 Field theories in dimensions other than four;
 Finitetemperature field theory;
 Expansions for large numbers of components;
 High Energy Physics  Phenomenology;
 Astrophysics;
 High Energy Physics  Theory;
 Nuclear Theory
 EPrint:
 27 Pages, 7 embedded .eps figures, uses epsf