G2 Yang-Mills理论中Dirac算子的手征对称性和谱性质
Chiral symmetry and spectral properties of the Dirac operator in G2 Yang-Mills Theory
摘要：
我们研究了具有平凡中心的特殊群G2的自发手征对称性破缺和交错格点Dirac算符的光谱性质。特别地，我们研究了有限温度跃迁以下和以上的系统，并使用费米子的时间边界条件来探测系统。我们评估几个可观察的：原点的谱密度、谱隙、手征凝聚体和最近提出的对偶手征凝聚体。我们表明，手征对称性在低温下被打破，并在高温下恢复在热力学相变。关于边界条件的作用，我们建立了G2的谱量在所有方面的行为与SU（N）完全相同，当对后一组，T_c以上的规范系综被限制在具有实Polyakov圈的位形扇区时。
英文摘要：
We study spontaneous chiral symmetry breaking and the spectral properties of the staggered lattice Dirac operator using quenched gauge configurations for the exceptional group G2, which has a trivial center. In particular we study the system below and above the finite temperature transition and use the temporal boundary conditions of the fermions to probe the system. We evaluate several observables: The spectral density at the origin, the spectral gap, the chiral condensate and the recently proposed dual chiral condensate. We show that chiral symmetry is broken at low temperatures and is restored at high temperatures at the thermodynamic phase transition. Concerning the role of the boundary conditions we establish that in all respects the spectral quantities behave for G2 in exactly the same way as for SU(N), when for the latter group the gauge ensemble above T_c is restricted to the sector of configurations with real Polyakov loop.
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