Topological solitons in a hot and dense fermi gas

Abstract

States with a fractional fermion number have been discovered in various relativistic field theory models, and in this paper the effects of a finite temperature and chemical potential are investigated. A general approach for the evaluation of the fermion number is developed and its various aspects are discussed; in particular the topological nature of the fermion number at finite temperature and chemical potential is revealed. The connection between the fermion number and the partition function of a hot and dense Fermi gas in the presence of a topologically nontrivial background is emphasized and the use of the fermion number as an order parameter is suggested. As an application, the solitons in the SU(2) × SU(2) Skyrme model are investigated, and it is suggested that the breakdown of the Skyrme model at high temperature and density can be related to the formation of a quark-gluon plasma in QCD. The critical values of the temperature and chemical potential are estimated in the adiabatic limit to be T c ≈ 100–300 MeV and μ c ≈ 300 MeV per quark.