论文标题
颗粒和字符串的牛顿 - 卡丹的概括性几何形状
Generalized Newton-Cartan Geometries for Particles and Strings
论文作者
论文摘要
我们讨论可以用作颗粒和字符串的引力背景场的广义牛顿 - 卡丹几何形状。为了使我们能够定义在结构组的所有对称性下不变的仿射连接，我们描述了具有独立扭转张子的扭转几何形状。我们认为的非Lorentzian几何形状的一个特征是，某些扭曲张量是所谓的“固有扭转”张量，这些张量无法在任何自旋连接中吸收。将这些固有扭转张量的某些组件设置为零，导致几何形状的限制。对于粒子和字符串，我们讨论了可以与结构组对称性一致施加的各种约束。这样，我们在文献中重现了几个结果。
We discuss the generalized Newton-Cartan geometries that can serve as gravitational background fields for particles and strings. In order to enable us to define affine connections that are invariant under all the symmetries of the structure group, we describe torsionful geometries with independent torsion tensors. A characteristic feature of the non-Lorentzian geometries we consider is that some of the torsion tensors are so-called `intrinsic torsion' tensors that cannot be absorbed in any of the spin connections. Setting some components of these intrinsic torsion tensors to zero leads to constraints on the geometry. For both particles and strings, we discuss various such constraints that can be imposed consistently with the structure group symmetries. In this way, we reproduce several results in the literature.
