Role of Dual Higgs Mechanism in Chiral Phase Transition at Finite Temperature

Abstract

The chiral phase transition at finite temperature is studied by using the Schwinger-Dyson equation in the dual Ginzburg-Landau theory, in which the dual Higgs mechanism plays an essential role on both the color confinement and the spontaneous chiral-symmetry breaking. At zero temperature, the quark condensate is strongly correlated with the string tension, which is generated by QCD-monopole condensation, as $⟨\bar{q}q{⟩}^{1/3}\stackrel{\propto }{\sim }\sqrt{\sigma }$. In order to solve the finite-temperature Schwinger-Dyson equation numerically, we provide a new ansatz for the quark self-energy in the imaginary-time formalism. The recovery of the chiral symmetry is found at high temperature; $T_{{}_C}\sim 100\mathrm{MeV}$ with realistic parameters. We find also a strong correlation between the critical temperature $T_{{}_C}$ of the chiral symmetry restoration and the strength of the string tension.

Comments: 12 pages, revtex (4 figures - available on request from ssasaki@rcnp.osaka-u.ac.jp)