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arXiv 2304.03357hep-th
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强耦合手征规范理论的动力学

Dynamics of strongly-coupled chiral gauge theories

Stefano Bolognesi, Kenichi Konishi, Andrea Luzio

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33 pages, 6 figures, proceeding for the conference AQFTCS 2022
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AI总结：

本文研究了渐近自由且规范反常无关的 $SU(N)$ 手征规范理论动力学，提出并验证了包括动力学 Higgs 相、动力学阿贝尔化及类箭袋规范理论在内的多种更一般的红外相结构。

摘要：

我们研究了包含属于对称、反对称或基础表示的各种组合的无质量费米子的 $SU(N)$ 手征规范理论的动力学。我们将自己限制在规范反常无关和渐近自由的系统内。't Hooft 反常匹配条件严格限制了可能的 RG 流。在矢量型理论（如量子色动力学）中，规范不变的“夸克-反夸克”凝聚形成并表征了红外动力学，且反常匹配涉及 Nambu-Goldstone 玻色子。在其他一些特殊情况下，如 Bars-Yankielowicz (BY) 或 Georgi-Glashow (GG) 模型，文献中提出了一种假设性解，即没有全局对称性破缺，且由一些简单的复合无质量费米子饱和所有反常。实际上，对于 BY 和 GG 系统，其红外物理更合理的候选者是动力学 Higgs 相，该相具有少数简单的双费米子色味锁定凝聚，部分或完全破坏色和味对称性。值得注意的是，'t Hooft 反常匹配（及广义反常匹配）条件在该相中自动满足。出现在某些手征规范理论中的另一个有趣可能性是动力学阿贝尔化，这在 ${\cal N}=2$ 超对称规范理论中为人熟知。我们在此探讨了比上述更广泛类别的模型中，比上述更一般类型的可能红外相。借助大 N 论证，我们寻找红外自由理论，而 MAC（最大吸引通道）判据可能暗示一些简单的双费米子凝聚表征了系统的红外动力学。在许多情况下，发现低能有效理论由类箭袋规范理论描述，其中一些（非阿贝尔）规范群是红外自由的，而另一些可能是渐近自由的。

英文摘要：

We study the dynamics of $SU(N)$ chiral gauge theories with massless fermions belonging to various combinations of the symmetric, antisymmetric or fundamental representations. We limit ourselves to the gauge-anomaly-free and asymptotically free systems. 't Hooft anomaly-matching conditions severely limit the possible RG flows. In vectorlike theories such as the quantum chromodynamics, gauge-invariant ``quark-antiquark" condensates form and characterize the IR dynamics, and the anomaly matching involves the Nambu-Goldstone bosons. In some other special cases, such as the Bars-Yankielowicz (BY) or Georgi-Glashow (GG) models, a hypothetical solution was proposed in the literature, with no global symmetry breaking and with some simple set of composite massless fermions saturating all the anomalies. For the BY and GG systems, actually, a more plausible candidate for their IR physics is the dynamical Higgs phase, with a few simple bi-fermion color-flavor locked condensates, breaking the color and flavor symmetries, partially or totally. Remarkably, the 't Hooft anomaly-matching (and generalized anomaly-matching) conditions are automatically satisfied in this phase. Another interesting possibility, occurring in some chiral gauge theories, is dynamical Abelianization, familiar from ${\cal N}=2$ supersymmetric gauge theories. We explore here even more general types of possible IR phases than the ones mentioned above, for wider classes of models. With the help of large-N arguments we look for IR free theories, whereas the MAC (maximal attractive channel) criterion might suggest some simple bi-fermion condensates characterizing the IR dynamics of the systems. In many cases the low-energy effective theories are found to be described by quiver-like gauge theories, some of the (nonAbelian) gauge groups are infrared-free while some others might be asymptotically free.

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