Gapless Dirac Spectrum at High Temperature

Abstract

Using the overlap Dirac operator I show that, contrary to some expectations, even well above the critical temperature there is not necessarily a gap in the Dirac spectrum in pure SU(2) gauge theory. This happens when the Polyakov loop and the fermion boundary condition combine to give close to periodic boundary condition for the fermions in the time direction. In this Polyakov loop sector there is a non-vanishing density of Dirac eigenvalues around zero which implies that chiral symmetry is spontaneously broken. I demonstrate this both directly and also by finding good agreement with the random matrix theory prediction for the distribution of the lowest Dirac eigenvalue. I show that the chiral condensate increases with the temperature therefore it is very unlikely to be explained by topological fluctuations that become rapidly smaller above T_c. Finally I show that it is only a small fraction of the lowest Dirac eigenvalues that decide which Polyakov loop sector is favored by the fermion determinant if dynamical fermions are turned on. This provides a qualitative understanding of how the loss of confinement above T_c implies the restoration of chiral symmetry.

8 pages, 4 Postscript figures, uses PoS documentclass

References in corpus (9)

• The QCD transition temperature: results with physical masses in the continuum limit
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• Complete spectra of the Dirac operator and their relation to confinement
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Cited by in corpus (4)

• Inverse magnetic catalysis and the Polyakov loop
• Fermionic boundary conditions and the finite temperature transition of QCD
• Spontaneous Chiral Symmetry Breaking as Condensation of Dynamical Chirality
• Chiral Symmetry Breaking and Chiral Polarization: Tests for Finite Temperature and Many Flavors