论文标题
纯纺纱和$ d = 11 $超级
Pure spinors and $D=11$ supergravity
论文作者
论文摘要
在这篇论文中，我们研究了使用纯旋转变量描述$ d = 11 $超重性的第一和第二定量的方法。我们通过BRST共同学参数从半光线孔量规$ d = 11 $ Brink-Schwarz类似于Superparpicle开始，介绍了所谓的$ d = 11 $ pure Spinor Superparticle。在对第三个幽灵的纯旋转BRST共同体进行轻锥分析后，我们发现$ d = 11 $ supergravity的线性运动方程在$ d = 9 $ superspace中。此外，我们构建了一个由全球字段制成的BRST封闭的，幽灵的第一顶顶点操作员和$ d = 11 $超级超级超级场地，当构造幽灵号零顶点操作员满足标准下降方程的幽灵数字时，我们遇到了不一致的情况。然后，我们介绍了$ d = 11 $纯的旋转超级粒子的非最低版本，其中可以构建一个复合$ b $ -ghost，以满足$ \ {q，b \} = p^{2} $。但是，其复杂的表达使得难以检查其效果。我们表明，引入$ SO（1,10）$ FERMIONIC VECTOR $ \barς^{a} $简化了$ b $ -GHOST的形式，这使我们能够验证$ \ {q，b \} = p^{2} $ \ {2} $ and $ \ \ \ {b，b，b \ \ \} = $ brst-ex-ex-ex-exact。使用此$ B $ -GHOST，我们提出了一个满足标准下降方程的替代性幽灵数零顶点操作员。但是，它的表达将以非常复杂的方式取决于非最小的纯旋转变量。在讨论了$ d = 11 $超级重力的这种首次量化方法之后，我们继续讨论Cederwall引入的纯旋转主操作，以研究最大程度的超对称规格理论。我们表明，这些动作确实描述了$ d = 10 $ super-yang-mills，$ d = 10 $ super-bar-bry-infeld和$ d = 11 $ supergravity，通过为每种理论提取普通超空的运动方程。
In this Thesis we study first- and second-quantized approaches describing $D=11$ supergravity using pure spinor variables. We introduce the so-called $D=11$ pure spinor superparticle through BRST cohomology arguments starting from the semi-light-cone gauge $D=11$ Brink-Schwarz-like superparticle. After performing a light-cone gauge analysis of the pure spinor BRST cohomology at ghost number three, we find the linearized equations of motion of $D=11$ supergravity in $D=9$ superspace. In addition, we construct a BRST-closed, ghost number one vertex operator made out of worldline fields and $D=11$ supergravity superfields, and we run into an inconsistency when constructing a ghost number zero vertex operator satisfying a standard descent equation. We then introduce the non-minimal version of the $D=11$ pure spinor superparticle, in which a composite $b$-ghost can be constructed satisfying $\{Q,b\} = P^{2}$. However, its complicated expression makes it difficult to check its nilpotency. We show that introducing an $SO(1,10)$ fermionic vector $\barΣ^{a}$ simplifies the form of the $b$-ghost considerably, which allows us to verify that $\{Q,b\} = P^{2}$ and $\{b,b\}=$ BRST-exact. Using this $b$-ghost we propose an alternative ghost number zero vertex operator satisfying a standard descent equation. However, its expression will depend on non-minimal pure spinor variables in a very complicated fashion. After discussing this first-quantized approach for $D=11$ supergravity, we move on to discussing the pure spinor master actions introduced by Cederwall for studying maximally supersymmetric gauge theories. We show that these actions indeed describe $D=10$ super-Yang-Mills, $D=10$ super-Born-Infeld and $D=11$ supergravity by extracting the equations of motion in ordinary superspace for each one of these theories.
