A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities

2015/12/19 by Hamid R. Afshar, Eric A. Bergshoeff, Aditya Mehra +2 · 1 citation
Physics and Astronomy · #hep-th

paper · pdf · doi:10.1007/jhep04(2016)145

35 pages + appendices

arxiv created 2015/12/19 · arxiv updated 2016/05/25

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 Hořava-Lifshitz gravity by classifying all possible Schrödinger invariant scalar field theories of a complex scalar up to second order in time derivatives.

Cited by

• Covariant Poisson's equation in torsional Newton-Cartan gravity

Related

• Torsional Newton-Cartan Geometry and the Schrödinger Algebra
• Higher Symmetries of the Schrödinger Operator in Newton-Cartan Geometry
• Notes on su(1,2)⊕u(1) Chern-Simons theory and Torsional Newton-Cartan gravity
• Newton-Cartan supergravity with torsion and Schrödinger supergravity
• Conformal Gravity as a Deformed Topological Field Theory