论文标题
$ {\ cal n} = 1 $ supersymmetry in $ 4D $重力与扭转和非金属度
${\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity
论文作者
论文摘要
我们研究了典型的自由度和$ {\ cal n} = 1 $ supersymmetry的4维流形中，并具有任意扭转和非金属张力张量，使连接变形。我们检查局部差异性，洛伦兹（Lorentz）的封闭，洛伦兹（Lorentz）和维埃尔比因（Vielbein）和雷神（Gravitino）的超对称转换在费米子（Fermions）的领先顺序上。作用在Vielbein上的一对超对称转换的闭合限制了自旋连接的形式。后者对基本领域的依赖性仅由Vielbein，直到洛伦兹和/或差异性括号，独立于仿真连接的扭转或非现值变形，这在此顺序不受超对称性的限制。然后，我们将Rarita-Schwinger理论的夫妇研究到了通用的引力Lagrangian。前者的超对称变化限制了玻色子拉格朗日的形式，以实现不变性。 $ r_ {μν} {}^{ab} = 0 $，$ q_ {μνρ} = 0 $或$ t_ {μν} {} {}^ρ= 0 $的特殊情况。
We study the inclusion of fermionic degrees of freedom and ${\cal N}=1$ supersymmetry in 4-dimensional manifolds with arbitrary torsion and non-metricity tensors deforming the connection. We inspect the closure of local diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and gravitino at leading order in fermions. The closure of a pair of supersymmetric transformations acting on the vielbein restricts the form of the spin connection. The dependency of the latter on the fundamental fields is exclusively given by the vielbein, up to Lorentz and/or diffeomorphisms brackets, independently of the torsion or non-metricity deformations of the affine connection, which is not restricted by supersymmetry at this order. We have then studied the couple of the Rarita-Schwinger theory to a generic gravitational Lagrangian; the supersymmetric variation of the former restricts the form of the bosonic Lagrangian in order to accomplish invariance. Special cases where $R_{μν}{}^{ab}=0$, $Q_{μνρ}=0$ or $T_{μν}{}^ρ=0$ are provided.
