标准模型的协边性与形变类
Cobordism and Deformation Class of the Standard Model
摘要：
在$d$ d时空中具有可逆整体对称性G（包括时空和内部对称性）的量子场论（QFT）的t Hooft反常被称为$d+1$ d配边群TP $_{d+1}$（G），其群生成元是写为可逆拓扑场论（iTFT）Z $_{d+1}$的$d+1$ d配边不变量.最近提出QFT的变形类由其对称性G和iTFT Z $_{d+1}$来描述。相同变形类的看似不同的QFT可以通过量子相变彼此变形。在这项工作中，我们问的变形类控制的4维未规范或规范（SU（3）$\times$ SU（2）$\times$ U（1））/ $\mathbb{Z}_q$标准模型（SM）的$q=1,2,3,6$连续或离散$(\bf{B}-\bf{L})$对称性。我们表明答案包含5d iTFT的一些组合：与$(\bf{B}-\bf{L})^3$和$(\bf{B}-\bf{L})$相关的两个$\mathbb{Z}$类-（重力）$^2$ 4d微扰局部异常，与4d非微扰全局异常相关的模16类Atiyah-Patodi-Singer $η$不变量和模2类Stiefel-Whitney $w_2w_3$不变量，以及涉及更高对称性的附加$\mathbb{Z}_3\times\mathbb{Z}_2$类，其带电对象是Wilson电或t Hooft磁力线算子。在局部反常的$\mathbb{Z}$类和24576类全局反常中，我们确定了一个SM形变类，它的标号为$(N_f,n_{ν_{R}},$ p $',q)$，中微子数族和“右手不育”中微子数，磁偶数据，以及mod $q$关系.大统一和超统一，用新的奇异的有隙/无隙扇区取代无菌中微子（例如，拓扑或共形场论）或具有拓扑或配边约束的引力扇区，所有都驻留在SM变形类中。SM附近的相邻相/转变/临界区表现出超越SM现象。
英文摘要：
't Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a $d$d spacetime are known to be classified by a $d+1$d cobordism group TP$_{d+1}$(G), whose group generator is a $d+1$d cobordism invariant written as an invertible topological field theory (iTFT) Z$_{d+1}$. The deformation class of QFT is recently proposed to be specified by its symmetry G and an iTFT Z$_{d+1}$. Seemingly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. In this work, we ask which deformation class controls the 4d ungauged or gauged (SU(3)$\times$SU(2)$\times$U(1))/$\mathbb{Z}_q$ Standard Model (SM) for $q=1,2,3,6$ with a continuous or discrete $(\bf{B}-\bf{L})$ symmetry. We show that the answer contains some combination of 5d iTFTs: two $\mathbb{Z}$ classes associated with $(\bf{B}-\bf{L})^3$ and $(\bf{B}-\bf{L})$-(gravity)$^2$ 4d perturbative local anomalies, a mod 16 class Atiyah-Patodi-Singer $η$ invariant and a mod 2 class Stiefel-Whitney $w_2w_3$ invariant associated with 4d nonperturbative global anomalies, and additional $\mathbb{Z}_3\times\mathbb{Z}_2$ classes involving higher symmetries whose charged objects are Wilson electric or 't Hooft magnetic line operators. Out of $\mathbb{Z}$ classes of local anomalies and 24576 classes of global anomalies, we pin down a deformation class of SM labeled by $(N_f,n_{ν_{R}},$ p$',q)$, the family and "right-handed sterile" neutrino numbers, magnetic monopole datum, and mod $q$ relation. Grand Unifications and Ultra Unification that replaces sterile neutrinos with new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or gravitational sectors with topological or cobordism constraints, all reside in an SM deformation class. Neighbor phases/transitions/critical regions near SM exhibit beyond SM phenomena.
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