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arXiv 1809.09773hep-thhep-lat
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固定$θ$角下QCD的Dirac谱和手征凝聚

Dirac spectrum and chiral condensate for QCD at fixed $θ$-angle

M. Kieburg, J. J. M. Verbaarschot, T. Wettig

备注：
20 pages, 11 figures
发表信息：
Phys. Rev. D 99, 074515 (2019)
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摘要：

我们分析了非零$θ$角下QCD手征凝聚的质量依赖性，发现手征凝聚的不连续性一般不依赖于Dirac谱的支撑.为了理解这种行为，我们将谱密度和手征凝聚分解为零模、淬灭部分和对费米子行列式敏感的剩余部分（称为动力学部分）的贡献。我们得到了零模贡献的一般公式。淬火部分的表达式，有效的任意数量的口味，和动力学部分，有效的一个和两个口味，来自微观领域的QCD。我们发现，在非零$θ$ -角的狄拉克谱密度的淬火和动力学部分强烈振荡的振幅，指数增加的体积$V$和周期的顺序为$1/V$。手征凝聚体的猝灭部分在$θ\ne0$处指数增大，但这种发散被零模的贡献所抵消。密度动力学部分的振荡行为对于将手征凝聚体的不连续性从狄拉克谱的支持中移开是必不可少的。作为这项工作的重要副产品，我们获得了非零$θ$ -角的狄拉克算子的微观谱密度的解析表达式，对于非零夸克质量的单味和双味QCD。

英文摘要：

We analyze the mass dependence of the chiral condensate for QCD at nonzero $θ$-angle and find that in general the discontinuity of the chiral condensate is not on the support of the Dirac spectrum. To understand this behavior we decompose the spectral density and the chiral condensate into contributions from the zero modes, the quenched part, and a remainder which is sensitive to the fermion determinant and is referred to as the dynamical part. We obtain general formulas for the contributions of the zero modes. Expressions for the quenched part, valid for an arbitrary number of flavors, and for the dynamical part, valid for one and two flavors, are derived in the microscopic domain of QCD. We find that at nonzero $θ$-angle the quenched and dynamical part of the Dirac spectral density are strongly oscillating with an amplitude that increases exponentially with the volume $V$ and a period of order of $1/V$. The quenched part of the chiral condensate becomes exponentially large at $θ\ne0$, but this divergence is canceled by the contribution from the zero modes. The oscillatory behavior of the dynamical part of the density is essential for moving the discontinuity of the chiral condensate away from the support of the Dirac spectrum. As important by-products of this work we obtain analytical expressions for the microscopic spectral density of the Dirac operator at nonzero $θ$-angle for both one- and two-flavor QCD with nonzero quark masses.

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