标题： ${\cal N}=1$在具有扭力和非度规性的$4D$引力中的超对称性 显示英文标题

标题： ${\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity

摘要： 我们研究在具有任意扭率和非度规张量的四维流形中包含费米自由度和${\cal N}=1$超对称性。 我们检查在费米子的高阶项中局部微分同胚、洛伦兹和超对称变换在vielbein和gravitino上的闭合性。 一对超对称变换作用在vielbein上的闭合性限制了自旋连接的形式。 后者对基本场的依赖性仅由vielbein给出，除了洛伦兹和/或微分同胚括号之外，与仿射连接的扭率或非度规变形无关，这些变形在此阶次下不受超对称性限制。 我们随后研究了Rarita-Schwinger理论与一般引力拉格朗日量的耦合；前者超对称变分限制了玻色拉格朗日量的形式以实现不变性。 提供了$R_{\mu \nu}{}^{ab}=0$、$Q_{\mu \nu \rho}=0$或$T_{\mu \nu}{}^{\rho}=0$的特殊情况。 显示英文摘要

摘要： 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 $R_{\mu \nu}{}^{ab}=0$, $Q_{\mu \nu \rho}=0$ or $T_{\mu \nu}{}^{\rho}=0$ are provided.