# Dirac Spectrum, Axial Anomaly and the QCD Chiral Phase Transition

## TL;DR

This paper investigates the Dirac spectrum and axial anomaly across the QCD chiral phase transition using lattice simulations, revealing unexpected chiral symmetry behavior in the high-temperature phase and effects of a new quenched quark species.

## Contribution

It introduces a new quenched quark species to study the Dirac spectrum and chiral symmetry breaking, providing novel insights into the phase transition and eigenvalue distribution.

## Key findings

- Small eigenvalues support anomalous chiral symmetry breaking above the critical temperature.
- Different Z3 phases exhibit distinct chiral behaviors in the deconfinement region.
- Unexpected chiral symmetry restoration in the real Z3 phase suggests new phase transition phenomena.

## 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.