论文标题
现代张量 - 螺旋符号符号代数算法和计算非闭合几何和整体数字11d,n = 1 supergravity
Modern Tensor-Spinor Symbolic Algebra Algorithms and Computing Non-Closure Geometry & Holoraumy in 11D, N = 1 Supergravity
论文作者
论文摘要
超对称基因组学项目旨在通过诸如Adinkras和holoraumy之类的属性对超级植物进行分类。该项目的协议是:1)设置具有未知数值系数的SUSY转换规则(和操作),2)求解这些系数,3)计算所需的属性,例如非关闭几何形状(非关闭的几何形状(在超级衍生物的抗强化剂的抗强化剂中起作用)和SuperCovariant of Supercovariant的抗性词性)。 This paper provides the first broadly applicable computer algorithms for completing these computations, comprising a new Cadabra module we call ``SusyPy.'' We provide a significant extension of the available tensor-arithmetic/canonicalization to include spinor-indexed expressions and NW-SE convention, and we provide a new Fierz expansion algorithm for spinor-indexed expressions.除了这个新的张量 - 旋转符号代数外,我们还构建了用于求解多重组系数及其动作的系数,以及计算Holoraumy的系数,用于脱壳和shell n = 1个尺寸的shell n = 1个多层。我们将工具应用于基因组学项目中的线性化11D,n = 1个超级重力。我们在几行代码中演示了求解11D,n = 1多重组,如Cremmer,Julia和Scherk中,我们提供了多个非关闭几何形状的全面图片。此外,我们提供了有史以来的11D全毛,n = 1个超级重力的计算。
The Supersymmetry Genomics project aims to classify supermultiplets by properties like adinkras and holoraumy. The project's protocol is: 1) set up the SUSY transformation rules (and action) with unknown numerical coefficients, 2) solve those coefficients, and 3) compute desired properties, e.g., non-closure geometry (the non-closure functions in the anticommutator of supercovariant derivatives) and holoraumy (the commutator of supercovariant derivatives). This paper provides the first broadly applicable computer algorithms for completing these computations, comprising a new Cadabra module we call ``SusyPy.'' We provide a significant extension of the available tensor-arithmetic/canonicalization to include spinor-indexed expressions and NW-SE convention, and we provide a new Fierz expansion algorithm for spinor-indexed expressions. On top of this new tensor-spinor symbolic algebra, we have built algorithms for solving for the coefficients of a multiplet and its action, and for computing holoraumy, for both off-shell and on-shell N = 1 multiplets of any dimension. We apply our tools to assimilate linearized 11D, N = 1 supergravity into the Genomics project. We demonstrate solving the 11D, N = 1 multiplet, as in Cremmer, Julia, and Scherk, in a few lines of code, and we provide a comprehensive picture of the multiplet's non-closure geometry. Further, we provide the first-ever computation of the holoraumy of 11D, N = 1 supergravity.