The geometric role of symmetry breaking in gravity

Details The geometric role of symmetry breaking in gravity The geometric role of symmetry breaking in gravity

2011-12-11

arxiv.org/abs/1112.2390v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

4 pages. Contribution written for proceedings of the conference "Loops 11" (Madrid, May 2011)

Scientific paper

In gravity, breaking symmetry from a group G to a group H plays the role of describing geometry in relation to the geometry the homogeneous space G/H. The deep reason for this is Cartan's "method of equivalence," giving, in particular, an exact correspondence between metrics and Cartan connections. I argue that broken symmetry is thus implicit in any gravity theory, for purely geometric reasons. As an application, I explain how this kind of thinking gives a new approach to Hamiltonian gravity in which an observer field spontaneously breaks Lorentz symmetry and gives a Cartan connection on space.

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