论文标题
自旋的几何形状（10）对称性破裂
Geometry of Spin(10) Symmetry Breaking
论文作者
论文摘要
我们提供了标准模型量规组GSM作为自旋的亚组的新表征（10）。 GSM的新描述依赖于纯纺纱的几何形状。我们表明，GSM是稳定纯旋转psi_1的子组，并在psi_1，psi_2正交中稳定了另一个纯旋转PSI_2，因此它们的任意线性组合仍然是纯旋转器。我们对GSM的表征依赖于射影纯旋转器描述r^{10}上的复杂结构的事实，而两个通勤复杂结构的乘积是所谓的产品结构。对于纯纺丝PSI_1，PSI_2满足所述条件，由PSI_1，PSI_2通勤和产生的产品结构确定的复杂结构为r^{10} = r^6 + r^4，从而产生了pati-salam量规组的副本（10）。然后，我们的主要陈述源于GSM是稳定PSI_1的Georgi-Glashow su（5）的相交，而pati-salam旋转（6）x spin（4）是由由psi_1，psi_2确定的产物结构引起的。我们试图使纸变得独立，并详细描述了Clifford代数CL（2N）的创建/歼灭操作员的构建和纯纺纱器的几何形状，直到包括十个。
We provide a new characterisation of the Standard Model gauge group GSM as a subgroup of Spin(10). The new description of GSM relies on the geometry of pure spinors. We show that GSM is the subgroup that stabilises a pure spinor Psi_1 and projectively stabilises another pure spinor Psi_2, with Psi_1, Psi_2 orthogonal and such that their arbitrary linear combination is still a pure spinor. Our characterisation of GSM relies on the facts that projective pure spinors describe complex structures on R^{10}, and the product of two commuting complex structures is a what is known as a product structure. For the pure spinors Psi_1, Psi_2 satisfying the stated conditions the complex structures determined by Psi_1, Psi_2 commute and the arising product structure is R^{10} = R^6 + R^4, giving rise to a copy of Pati-Salam gauge group inside Spin(10). Our main statement then follows from the fact that GSM is the intersection of the Georgi-Glashow SU(5) that stabilises Psi_1, and the Pati-Salam Spin(6) x Spin(4) arising from the product structure determined by Psi_1, Psi_2. We have tried to make the paper self-contained and provided a detailed description of the creation/annihilation operator construction of the Clifford algebras Cl(2n) and the geometry of pure spinors in dimensions up to and including ten.
