论文标题
卡罗尔与伽利略从勃雷恩的角度来看
Carroll versus Galilei from a Brane Perspective
论文作者
论文摘要
我们表明，我们以前在Galilei和Carroll Gravity（易于颗粒）上的工作可以推广到Galilei和Carroll重力理论适应P-Branes（P = 0，1，2，...）。从这个更广阔的brane角度来看，我们利用文献中给出的形式图，在相应的p-brane carroll和galilei代数之间，其中描述了纵向纵向（横向）到galilei brane的指数与指数覆盖横向（纵向）的指数中的指数互动，从而始终是与横向的距离，从而使得时间远距离远距离，以至于时间远距离的时间是远距离的时间。这将3D中的其他事物带到了Galilei颗粒和Carroll字符串之间的地图，以及4D的地图到Galilei Strings和Carroll Strings之间的类似地图。我们表明，这张形式的地图扩展到了庞加莱代数的相应谎言代数扩展，因此扩展到了卡罗尔和加利利代数的几个扩展，包括中央扩展。我们使用此正式地图来构建几个新的Carroll重力动作示例。此外，我们在P-Brane Sigma模型动作水平上讨论了Carroll和Galilei之间的对称性，并应用这种形式的对称性，以在弯曲的Carroll背景下给出几个3D和4D颗粒和字符串的例子。
We show that our previous work on Galilei and Carroll gravity, apt for particles, can be generalized to Galilei and Carroll gravity theories adapted to p-branes (p = 0, 1, 2, ...). Within this wider brane perspective, we make use of a formal map, given in the literature, between the corresponding p-brane Carroll and Galilei algebras where the index describing the directions longitudinal (transverse) to the Galilei brane is interchanged with the index covering the directions transverse (longitudinal) to the Carroll brane with the understanding that the time coordinate is always among the longitudinal directions. This leads among other things in 3D to a map between Galilei particles and Carroll strings and in 4D to a similar map between Galilei strings and Carroll strings. We show that this formal map extends to the corresponding Lie algebra expansion of the Poincaré algebra and, therefore, to several extensions of the Carroll and Galilei algebras including central extensions. We use this formal map to construct several new examples of Carroll gravity actions. Furthermore, we discuss the symmetry between Carroll and Galilei at the level of the p-brane sigma model action and apply this formal symmetry to give several examples of 3D and 4D particles and strings in a curved Carroll background.
