论文标题
测量程序和卡洛利亚重力
The gauging procedure and carrollian gravity
论文作者
论文摘要
我们讨论了一个测量程序,该程序使我们能够构造决定基础cartan几何形状动态的拉格朗日人。从某种意义上说,在论文中精确地制作,测量过程中的启动数据是对应于同质空间的klein对。测量过程的等同于在klein几何形状上建立的cartan几何形状的构建,仪表场定义了cartan连接。 Lagrangian本身由所有根据Cartan连接及其曲率构建的量规不变的顶级形式组成。在证明该过程在测量Minkowski时空时产生了四维一般相对论,我们继续衡量所有四维最大对称的Carrollian空间:Carroll,(抗)de Sitter--carroll--carroll--carroll和Lightcone。对于这些空间的前三个,我们的拉格朗日人概括了早期的一阶拉格朗日。由此产生的卡洛利亚重力理论都采用相同的形式,这似乎是拉格朗日级别上模型突变的一种体现。奇怪的一个,即灯酮,不是还原性的,这意味着尽管运动方程的形式与其他情况相同,但几何解释是不同的。对于所有Carrollian重力理论,我们都会获得高斯 - Bonnet,Pontryagin和Nieh- Yan拓扑术语的类似物,以及其他本质上是Carrollian且似乎没有Lorentzian对应物的另外两个术语。由于我们从头开始衡量理论,因此在一阶配方中,这项工作也为电理论提供了无关的结果。
We discuss a gauging procedure that allows us to construct lagrangians that dictate the dynamics of an underlying Cartan geometry. In a sense to be made precise in the paper, the starting datum in the gauging procedure is a Klein pair corresponding to a homogeneous space. What the gauging procedure amounts to is the construction of a Cartan geometry modelled on that Klein geometry, with the gauge field defining a Cartan connection. The lagrangian itself consists of all gauge-invariant top-forms constructed from the Cartan connection and its curvature. After demonstrating that this procedure produces four-dimensional General Relativity upon gauging Minkowski spacetime, we proceed to gauge all four-dimensional maximally symmetric carrollian spaces: Carroll, (anti-)de Sitter--Carroll and the lightcone. For the first three of these spaces, our lagrangians generalise earlier first-order lagrangians. The resulting theories of carrollian gravity all take the same form, which seems to be a manifestation of model mutation at the level of the lagrangians. The odd one out, the lightcone, is not reductive and this means that although the equations of motion take the same form as in the other cases, the geometric interpretation is different. For all carrollian theories of gravity we obtain analogues of the Gauss--Bonnet, Pontryagin and Nieh--Yan topological terms, as well as two additional terms that are intrinsically carrollian and seem to have no lorentzian counterpart. Since we gauge the theories from scratch this work also provides a no-go result for the electric carrollian theory in a first-order formulation.