[论文解读] Topological Origin of Chiral Symmetry Breaking in QCD and in Gravity

Gia Dvali|arXiv (Cornell University)|May 17, 2017

Particle physics theoretical and experimental studies参考文献 22被引用 4

一句话总结

本文提出，在无费米子的量子色动力学（QCD）与引力理论中，真空拓扑敏感度足以在费米子凝聚时动态地实现手征对称性自发破缺，而无需依赖禁闭机制。研究显示轴向U(1)对称性变为异常，导致出现一个有质量的伪戈尔戈斯玻色子（类似于QCD中的η′粒子），且费米子通过三形式希格斯机制被从低能谱中动态移除，从而通过拓扑动力学统一了QCD与引力中手征对称性破缺的起源。

ABSTRACT

We show that the assumption of non-zero topological susceptibility of the vacuum in a fermion-free version of a theory, such as gravity or QCD, suffices to conclude the following: Once N massless fermion flavors are added to the theory, they break the chiral flavor symmetry dynamically, down to a subgroup that would be anomaly-free under gauging; In both theories, the pseudo-Goldstone corresponding to axial U(1)-symmetry becomes massive; In QCD as well as in gravity the massless fermions are eliminated from the low energy spectrum of the theory. All the above conclusions are reached without making an assumption about confinement. Some key methods of our approach are: Reformulation of topological susceptibility in the language of a three-form gauge theory; Utilization of gravity in the role of a spectator interaction for the chiral anomaly-matching in QCD; Gauging chiral symmetries and matching their anomalies using the spectator Green-Schwarz type axions. Our observations suggest that breaking of chiral symmetries in QCD and in gravity can be described in unified topological language, and seemingly-disconnected phenomena, such as, the generation of eta'-meson mass in QCD and breaking of global chiral symmetry by gravity may share a secret analogy. The described phenomenon may shed a new light - via contribution of micro black holes into the gravitational topological susceptibility of the vacuum - on incompatibility between black holes and global symmetries. It appears that explicit breaking is not the sole possibility, and like QCD, gravity may break global symmetries dynamically. As an useful byproduct, matching of gravitational anomalies provides a selection tool for compositeness, eliminating possibility of massless composite fermions where standard gauge anomaly matching would allow for their existence.

研究动机与目标

• 建立仅凭真空拓扑敏感度——无需禁闭——即可在QCD与引力中触发动力学手征对称性破缺的理论依据。
• 通过拓扑机制统一解释QCD中η′粒子质量与引力中手征对称性破缺的起源。
• 证明费米子通过三形式希格斯机制被动态地从低能谱中移除。
• 探讨微观黑洞对引力拓扑敏感度及手征对称性破缺的贡献作用。
• 通过引力反常匹配提供复合性的选择标准，排除标准反常匹配允许存在的无质量复合费米子。

提出的方法

• 将拓扑敏感度重新表述为三形式 gauge 理论，以描述伪标量模的希格斯机制。
• 将引力作为旁观者相互作用，用于匹配QCD中的手征反常，从而通过格林-施瓦茨型轴子实现反常匹配。
• 应用三形式希格斯机制，表明异常U(1)A对称性的名义戈尔戈斯玻色子获得质量。
• 利用引力手征反常表明所有费米子种类均普遍发生凝聚，其中轻费米子（如中微子）对效应最为敏感。
• 分析微观黑洞对真空拓扑敏感度的贡献，表明其可能抑制真空能量并促成对称性破缺。
• 利用旁观者轴子的反常匹配，排除具有引力反常的理论中无质量复合费米子的可能性。

实验结果

研究问题

• RQ1 仅凭真空拓扑敏感度，无需禁闭，是否足以在QCD中触发动力学手征对称性破缺？
• RQ2 是否存在一种统一的拓扑机制，可同时解释QCD中η′粒子质量与引力中手征对称性破缺？
• RQ3 微观黑洞如何贡献于引力拓扑敏感度及费米子凝聚？
• RQ4 通过旁观者轴子实现的引力反常匹配，是否能排除异常自由理论中无质量复合费米子的存在？
• RQ5 三形式希格斯机制在QCD与引力中生成伪戈尔戈斯玻色子质量的过程中起何种作用？

主要发现

• 在无费米子的理论中，非零的真空拓扑敏感度足以在引入Nf个无质量费米子味后，诱导动力学手征对称性破缺。
• 轴向U(1)A对称性被动力地破缺，其名义戈尔戈斯玻色子通过三形式希格斯机制获得质量，类似于QCD中η′粒子的质量生成机制。
• 费米子因凝聚而从低能谱中被移除，与红外区无无质量费米子的观测一致。
• 微观黑洞对引力拓扑敏感度有显著贡献，提示在非禁闭引力中存在手征对称性破缺的机制。
• 引力手征反常导致所有费米子种类普遍凝聚，其中中微子对效应最为敏感。
• 利用旁观者轴子的引力反常匹配提供了一项选择规则，可排除无质量复合费米子的存在，即使标准反常匹配允许其存在。