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Dirac spectrum, axial anomaly and the QCD chiral phase transition

Nuclear Physics B - Proceedings Supplements
Publication Date
DOI: 10.1016/0920-5632(96)00115-6
  • Physics


The QCD phase transition is studied on 16 3 and 32 3 × 4 lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark ζ and study the resulting chiral condensate, 〈 ζ ¯ ζ 〉 as a function of the ζ mass, m ζ . By examining 〈 ζ ¯ ζ 〉 for 10 −10 ≤ m ζ ≤ 10 we gain considerable information about the spectrum of Dirac eigenvalues. A comparison of ma = 0.01 and 0.025 shows little dependence of the Dirac spectrum on such a light, dynamical quark mass, after an overall shift in β is removed. The presence of sufficient small eigenvalues to support anomalous chiral symmetry breaking in the high temperature phase is examined quantitatively. In an effort to enhance these small eigenvalues, 〈 ζ ¯ ζ 〉 is also examined in the pure gauge theory in the region of the deconfinement transition with unexpected results. Above the critical temperature, the three Z 3 phases show dramatically different chiral behavior. Surprisingly, the real phase shows chiral symmetry, suggesting that a system with one flavor of staggered fermion at N t = 4 will possess a chiral a phase transition—behavior not expected in the continuum limit.

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