超越六维旋量的标准模型
Beyond the standard model with six-dimensional spinors
摘要：
利用具有$Spin(3,3)$对称性的6D旋量来有效地编码三代物质。$E_{8(-24)}$被证明包含物理上相关的子群表示为大统一体群，时空对称性，三代的标准模型费米子，希格斯玻色子。Pati-Salam、$SU(5)$和$Spin(10)$大统一理论是在孤立的一代中发现的。对于时空对称性，$Spin(4,2)$可以用于共形对称，$AdS_5\rightarrow dS_4$，或简单地破缺为闵可夫斯基空间的$Spin(3,1)$。另一类表示找到了$Spin(2,2)$，并可以给出具有各种GUT的$AdS_3$。在$E_{8(-24)}$内部具有$Spin(3)$味对称性的情况下，发现了三代费米子在$Spin(4,12)$的Majorana-Weyl旋量${\bf 128}$中的作用. $Spin(4,12)$的${\bf 128}$可以看作是一个特殊的伪黎曼形式的正八元数罗森菲尔德投影平面$E_{8(-24)}/Spin(4,12)= (\mathbb{O}_s\times\mathbb{O})\mathbb{P}^2$的切空间。
英文摘要：
6D spinors with $Spin(3,3)$ symmetry are utilized to efficiently encode three generations of matter. $E_{8(-24)}$ is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati-Salam, $SU(5)$, and $Spin(10)$ grand unified theories are found when a single generation is isolated. For spacetime symmetries, $Spin(4,2)$ may be used for conformal symmetry, $AdS_5\rightarrow dS_4$, or simply broken to $Spin(3,1)$ of Minkowski space. Another class of representations finds $Spin(2,2)$ and can give $AdS_3$ with various GUTs. An action for three generations of fermions in the Majorana-Weyl spinor ${\bf 128}$ of $Spin(4,12)$ is found with $Spin(3)$ flavor symmetry inside $E_{8(-24)}$. The ${\bf 128}$ of $Spin(4,12)$ can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane $E_{8(-24)}/Spin(4,12)= (\mathbb{O}_s\times\mathbb{O})\mathbb{P}^2$.
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。
