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arXiv · 1512.06277

A Schr\"odinger approach to Newton-Cartan and Ho\v{r}ava-Lifshitz gravities

Hamid R. Afshar·Eric A. Bergshoeff·Aditya Mehra·Pulastya Parekh·Blaise Rollier
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Abstract

We define a `non-relativistic conformal method', based on a Schr\"odinger algebra with critical exponent z = 2, as the non-relativistic version of the relativistic conformal method. An important ingredient of this method is the occurrence of a complex compensating scalar field that transforms under both scale and central charge transformations. We apply this non-relativistic method to derive the curved space Newton-Cartan gravity equations of motion with twistless torsion. Moreover, we reproduce z = 2 Ho\v{r}ava-Lifshitz gravity by classifying all possible Schr\"odinger invariant scalar field theories of a complex scalar up to second order in time derivatives.

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Hamid R. Afshar, Eric A. Bergshoeff, Aditya Mehra, Pulastya Parekh, Blaise Rollier. 2015-12-19. A Schr\"odinger approach to Newton-Cartan and Ho\v{r}ava-Lifshitz gravities. https://doi.org/10.1007/jhep04(2016)145

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