The geometric role of symmetry breaking in gravity

Abstract

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.

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

Cited by in corpus (9)

• Lifting General Relativity to Observer Space
• Cartan gravity, matter fields, and the gauge principle
• Generalized supersymmetric cosmological term in N=1 Supergravity
• Cartan geometry of spacetimes with a nonconstant cosmological function $\Lambda$
• Linking Covariant and Canonical General Relativity via Local Observers
• Contracted Lorentz invariance for gravity with a preferred foliation
• Probing Primordial Symmetry Breaking with Cosmic Microwave Background Anisotropy
• Geometrodynamics and Lorentz symmetry
• Spontaneous breaking of Lorentz symmetry for canonical gravity