Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions
Adjoint QCD on ℝ3 × S1 with twisted fermionic boundary conditions
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DOI：
10.1007/jhep06(2014)181
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发表时间：
2014-05
影响因子：
5.4
通讯作者：
T. Misumi;T. Kanazawa
中科院分区：
文献类型：
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作者：
T. Misumi;T. Kanazawa
我们研究了 ℝ 3× S 1 上伴随狄拉克费米子的 QCD，以及沿 S 1 的费米子通用边界条件。通过微扰理论、半经典方法和手性有效模型，我们阐明了由 S 1 致密尺度 L、扭曲费米子边界条件 phi 和费米子质量 m 跨越的空间中丰富的相结构。我们发现了具有或不具有手性和中心对称性破缺的各种相，由一阶和二阶相变分隔，在特定限制（Φ= 0、Φ= π、L→ 0 和 m→∞）下再现了文献中的已知结果。在小 L 的中心对称相中，我们表明 Ünsal 的生物诱导限制机制正在发挥作用，但在 Φ= 0 时被单极子之间的线性势大大削弱。通过对 PNJL 模型的分析和数值研究，我们表明中心对称性和手性对称性（即 Polyakov 环和手性凝聚体）的有序参数在 phi= 0 时强烈地交织在一起。由于这种相关性，解限相可以介入小 L 处的弱耦合中心对称相和大 L 处的强耦合中心对称相之间。这种情况是否发生取决于动力学的比率费米子质量到杨-米尔斯理论的能量尺度。简要讨论了规范理论复兴的可能性的含义。在附录中，我们研究了具有扭曲边界条件的ℝ 3× S 1 上的伴随狄拉克算子的指数，这对于单极子的半经典分析非常重要。
We investigate QCD with adjoint Dirac fermions on ℝ 3× S 1 with generic boundary conditions for fermions along S 1. By means of perturbation theory, semiclassical methods and a chiral effective model, we elucidate a rich phase structure in the space spanned by the S 1 compactification scale L, twisted fermionic boundary condition ϕ and the fermion mass m. We found various phases with or without chiral and center symmetry breaking, separated by first-and second-order phase transitions, which in specific limits (ϕ= 0, ϕ= π, L→ 0 and m→∞) reproduce known results in the literature. In the center-symmetric phase at small L, we show that Ünsal’s bion-induced confinement mechanism is at work but is substantially weakened at ϕ= 0 by a linear potential between monopoles. Through an analytic and numerical study of the PNJL model, we show that the order parameters for center and chiral symmetries (ie, Polyakov loop and chiral condensate) are strongly intertwined at ϕ= 0. Due to this correlation, a deconfined phase can intervene between a weak-coupling center-symmetric phase at small L and a strong-coupling one at large L. Whether this happens or not depends on the ratio of the dynamical fermion mass to the energy scale of the Yang-Mills theory. Implication of this possibility for resurgence in gauge theories is briefly discussed. In an appendix, we study the index of the adjoint Dirac operator on ℝ 3× S 1 with twisted boundary conditions, which is important for semiclassical analysis of monopoles.