论文标题
异常和恢复性限制超出了大统一：能量等级制度
Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
论文作者
论文摘要
最近的一项工作[2006.16996]表明，Mod 16类的4D非扰动全局异常暗示了一个可能的新的隐藏式间隙拓扑部门，超出了标准模型（SM）和Georgi-Glashow $ su（5）$ su（5）$ Grand Unifice Theory（Grandifiend Theory（ut）15n chiral Weyl fermions and serm serm and sermem and serm and serm and serm and serme and semer of disceet $ \ z} $ x = 5（{\ bf b- l}）-4y $。这个$ \ mathbb {z} _ {16} $ class Global Anomaly是离散$ x $和时空背景之间的混合量规范异常。新的拓扑部门具有肠道尺度的高能量差距，低于其低能的低能量编码4D不可拓扑量子量子场理论（TQFT）或5D短距离纠缠的可逆TQFT或它们的组合。这个隐藏的拓扑部门提供了缺失的无菌右撇子中微子（第16世代的Weyl fermions）的hooft异常匹配，并且可能还解释了暗物质部门。在SM和$ SU（5）$ ut中，离散的$ x $可以是全球对称性或测量。在$ so（10）$ ut中，$ x $必须变成量子，5D TQFT变成了不可理解且远程纠缠（可以将它们搭配到动态重力）。在这项工作中，我们进一步研究了高于$ su（5）$ ut to $ so（10）$ gut和$ so（18）$ ut（带有旋转（10）和旋转（10）和旋转（18）量规组）的较高能量尺度的异常和恢复限制。我们还发现[2006.16996]对新的隐藏间隙拓扑领域的提议可能与能量/质量层次结构下的异常匹配一致。调整能量的新成分包括无异常的对称质量产生的各种能量尺度（即Kitaev-Wen机制），这是来自异常对称拓扑秩序的拓扑质量/能量差距肠道与新的拓扑领域。
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.
