arXiv 2008.064992020-08-14hep-thcond-mat.supr-conhep-phmath.AT

Anomaly与超越大一统的协约主义约束：能量等级

Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy

Juven Wang

备注：: 50 pages. Primers: arXiv:2006.16996, arXiv:1910.14668, arXiv:1810.00844, arXiv:1809.11171

摘要：

最近的一项工作[2006.16996]表明，一个mod 16类的4d非微扰全局异常暗示了一个可能的新的隐藏的有隙拓扑扇区，超越了标准模型（SM）和Georgi-Eschhow $su(5)$大统一理论（GUT），具有15 n手征Weyl费米子和$X=5({\bf B- L})-4Y$的离散$su(5)$对称性。这种$\mathbb{Z}_{16}$类全球异常是离散的$X$和时空背景之间的混合规范重力异常。新的拓扑扇区具有GUT尺度的高能隙，在其低能量下编码4d不可逆拓扑量子场论（TQFT）或5d短程纠缠可逆TQFT，或它们的组合。这个隐藏的拓扑扇区提供了缺少的无菌右手中微子（第16代外尔费米子的3代）的特胡夫特异常匹配，也可能解释了暗物质扇区。在SM和$su(5)$ GUT中，离散的$X$可以是全局对称的，也可以是规范的。在$so(10)$大统一理论中，$X$必须被规范化，5d TQFT变得不可逆和长距离纠缠（这可以耦合到动力学引力）。在这项工作中，我们进一步研究了在更高的能量标度以上的$su(5)$ GUT到$so(10)$ GUT和$so(18)$ GUT（自旋（10）和自旋（18）规范群精确）的异常和配边约束。我们还发现[2006.16996]关于新的隐隙拓扑扇区的建议可以与能量/质量层次下的异常匹配相一致。沿着调整能量的新成分包括各种无异常对称质量产生的能量尺度（即，Kitaev-Wen机制）、来自异常对称拓扑序的拓扑质/能隙（可附接到5d $\mathbb{Z}_{4,X}$对称拓扑超导体）、可能的拓扑量子相变以及包括具有新拓扑扇区的GUT的超统一。

英文摘要：

A recent work [2006.16996] suggests that a 4d nonperturbative global anomaly of mod 16 class hinting a possible new hidden gapped topological sector beyond the Standard Model (SM) and Georgi-Glashow $su(5)$ Grand Unified Theory (GUT) with 15n chiral Weyl fermions and a discrete $\mathbb{Z}_{4,X}$ symmetry of $X=5({\bf B- L})-4Y$. This $\mathbb{Z}_{16}$ class global anomaly is a mixed gauge-gravitational anomaly between the discrete $X$ and spacetime backgrounds. The new topological sector has a GUT scale high energy gap, below its low energy encodes either a 4d noninvertible topological quantum field theory (TQFT), or a 5d short-range entangled invertible TQFT, or their combinations. This hidden topological sector provides the 't Hooft anomaly matching of the missing sterile right-handed neutrinos (3 generations of 16th Weyl fermions), and possibly also accounts for the Dark Matter sector. In the SM and $su(5)$ GUT, the discrete $X$ can be either a global symmetry or gauged. In the $so(10)$ GUT, the $X$ must become gauged, the 5d TQFT becomes noninvertible and long-range entangled (which can couple to dynamical gravity). In this work, we further examine the anomaly and cobordism constraints at higher energy scales above the $su(5)$ GUT to $so(10)$ GUT and $so(18)$ GUT (with Spin(10) and Spin(18) gauge groups precisely). We also find [2006.16996]'s proposal on new hidden gapped topological sectors can be consistent with anomaly matching under the energy/mass hierarchy. Novel ingredients along tuning the energy include various energy scales of anomaly-free symmetric mass generation (i.e., Kitaev-Wen mechanism), the Topological Mass/Energy Gap from anomalous symmetric topological order (attachable to a 5d $\mathbb{Z}_{4,X}$-symmetric topological superconductor), possible topological quantum phase transitions, and Ultra Unification that includes GUT with new topological sectors.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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