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Paper IPM / P / 15110  


Abstract:  
We define a `nonrelativistic conformal method', based on a Schrödinger algebra with critical exponent z = 2, as the nonrelativistic 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 nonrelativistic method to derive the curved space NewtonCartan gravity equations of motion with twistless torsion. Moreover, we reproduce z = 2 HoravaLifshitz 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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