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Paper   IPM / Physic / 15110
School of Physics
  Title:   A Schrodinger approach to Newton-Cartan and Horava-Lifshitz gravities
  Author(s): 
1.  H.R. Afshar
2.  E.A. Bergshoeff
3.  A. Mehra
4.  P. Parekh
5.  B. Rollier
  Status:   Published
  Journal: JHEP
  Vol.:  04
  Year:  2016
  Pages:   145
  Supported by:  IPM
  Abstract:
We define a `non-relativistic conformal method', based on a Schrödinger 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 Horava-Lifshitz gravity by classifying all possible Schrödinger invariant scalar field theories of a complex scalar up to second order in time derivatives.

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