论文标题
超越六维旋转器的标准模型
Beyond the standard model with six-dimensional spinors
论文作者
论文摘要
具有$ spin（3,3）$对称性的6D旋转器可有效编码三代物质。 $ e_ {8（-24）} $显示包含具有肠组的表示，时空对称性，三代标准模型费米子和希格斯玻色子的物理相关子组。帕蒂 - 萨拉姆（Pati-Salam），$ su（5）$和$ spin（10）$ grand Unified理论是隔离的。对于时空对称性，$ spin（4,2）$可用于保形对称性，$ ads_5 \ rightarrow ds_4 $，或者简单地分解为Minkowski Space的$ spin（3,1）$。另一类表示$ spin（2,2）$，并且可以用各种胆量给出$ ads_3 $。在Majorana-Weyl Spinor $ {\ bf 128} $ $ spin（4,12）$中的三代费米子的动作是$ spin（3）$ spin（3）$ e_ e_ {8（-24）} $中的$ spin（3）$。 $ spin（4,12）$的$ {\ bf 128} $可以被视为octo-octonionic rosenfeld Phoffeld Phoffeld Phoffeld Phoffeld Phoffeld Plactive Phoffeld $ e_ {8（-24）}/spin（4,12）= 4,12）= 4,12）= 4,12 = 4,12）= （\ Mathbb {o} _s \ Times \ Times \ Mathbb {O}）\ Mathbb {p}^2 $。
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 $E_{8(-24)}/Spin(4,12)= (\mathbb{O}_s\times\mathbb{O})\mathbb{P}^2$.
