## Abstract

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrodinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrodinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrodinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

Original language | English |
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Article number | 194 |

Number of pages | 20 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 10 |

DOIs | |

Publication status | Published - 27-Oct-2017 |

## Keywords

- Classical Theories of Gravity
- Space-Time Symmetries