Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

Abstract

The QCD phase transition is studied on $16^3$ and $32^3\times 4$ lattices both with and without quark loops. We introduce a new zero-flavor or quenched species of quark $\zeta$ and study the resulting chiral condensate, $\azbz$ as a function of the $\zeta$ mass, $m_{\zeta }$. By examining $\azbz$ for $10^{-10}\le m_{\zeta }\le 10$ 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 $\beta$ 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, $\azbz$ 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.

Contribution to Lattice 95. 8 pages. Latex source file Individual figures available from [email protected] and also submitted seperately as figures.uu as required!

References in corpus (1)

• Finite temperature QCD: progress and outstanding problems

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