高温下的无隙Dirac谱
Gapless Dirac Spectrum at High Temperature
摘要：
利用重叠狄拉克算符，我证明了，与某些期望相反，在纯SU（2）规范理论中，即使在临界温度以上，狄拉克谱也不一定有能隙。当Polyakov环和费米子边界条件结合起来，在时间方向上给出费米子的周期性边界条件时，就会发生这种情况。在这个Polyakov环扇区中，狄拉克本征值在零附近有一个非零密度，这意味着手征对称性自发破缺。我证明了这两个直接，也找到很好的协议与随机矩阵理论预测的最低狄拉克本征值的分布。我证明了手征凝聚体随温度的升高而增加，因此它不太可能用拓扑涨落来解释，拓扑涨落在T_c以上迅速变小。最后，我们证明了只有最低Dirac本征值的一小部分决定了当动力学费米子开启时，费米子行列式对Polyakov圈的哪一个扇区有利，这就从定性上理解了T_c以上禁闭的丧失意味着手征对称性的恢复。
英文摘要：
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.
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