arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1504.07461hep-thgr-qc
收藏

动力学Newton-Cartan几何中的Horava-Lifshitz引力

Horava-Lifshitz Gravity From Dynamical Newton-Cartan Geometry

Jelle Hartong, Niels A. Obers

摘要:

最近已经确定扭转牛顿-卡当(TNC)几何是非相对论场论耦合的适当几何框架。我们表明,当这些几何是动态的,他们会引起Horava-Lifshitz(HL)引力。可投射HL引力对应于无挠的动力学牛顿-Cartan(NC)几何,不可投射HL引力对应于无挠的动力学NC几何(超曲面正交叶理)。我们建立了一个精确的字典有关的所有领域(包括标量khronon),他们的变换和其他性质的HL重力和动态TNC几何。我们利用TNC不变性构造了2+1维动力学指数为1<z \le 2的无扭扭Newton-Cartan几何的有效作用量,并证明了这与文献中构造的HL作用量的最一般形式完全一致.此外,我们确定了Horava和Melby-Thompson观察到的U(1)对称性的起源来自局部伽利略代数的Bargmann扩展,该扩展作用于TNC几何的切空间。我们认为,TNC几何,这是明显的同胚协变,是一个自然的几何框架HL引力,并讨论了它的一些影响。

英文摘要:

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Horava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1<z\le 2 and demonstrate that this exactly agrees with the most general forms of the HL actions constructed in the literature. Further, we identify the origin of the U(1) symmetry observed by Horava and Melby-Thompson as coming from the Bargmann extension of the local Galilean algebra that acts on the tangent space to TNC geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑