(Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects

Abstract

Space-time symmetries are a crucial ingredient of any theoretical model in physics. Unlike internal symmetries, which may or may not be gauged and/or spontaneously broken, space-time symmetries do not admit any ambiguity: they are gauged by gravity, and any conceivable physical system (other than the vacuum) is bound to break at least some of them. Motivated by this observation, we study how to couple gravity with the Goldstone fields that non-linearly realize spontaneously broken space-time symmetries. This can be done in complete generality by weakly gauging the Poincare symmetry group in the context of the coset construction. To illustrate the power of this method, we consider three kinds of physical systems coupled to gravity: superfluids, relativistic membranes embedded in a higher dimensional space, and rotating point-like objects. This last system is of particular importance as it can be used to model spinning astrophysical objects like neutron stars and black holes. Our approach provides a systematic and unambiguous parametrization of the degrees of freedom of these systems.

arXiv comment30 pages

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• Gapped Goldstones at the cut-off scale: a non-relativistic EFT
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• Gauging nonrelativistic field theories using the coset construction
• More on the operator-state map in non-relativistic CFTs
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• From QCD Strings to WZW
• Gravitational Dressing of 3D Conformal Galileon
• Inequivalence of Coset Constructions for Spacetime Symmetries: Coupling with Gravity
• The coset construction for particles of arbitrary spin
• Effective field theory for the superfluid vortex lattice from coset construction