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2011

The geometric role of symmetry breaking in gravity

Wise, Derek K.

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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.

The geometric role of symmetry breaking in gravity · Around

Built on

S. W. MacDowell and F. Mansouri, Unified geometric theory of gravity and supergravity, Phys. Rev. Lett
1977
Earlier work this paper cites.
K. S. Stelle and P. C. West, De Sitter gauge invariance and the geometry of the Einstein–Cartan theory, J. Phys. A: Math. Gen
1980
Earlier work this paper cites.
R. B. Gardner, The Method of Equivalence and its Applications
1989
Earlier work this paper cites.

Similar

J. D. Romano, Geometrodynamics vs. connection dynamics, Gen. Rel. Grav
1993
Cited alongside, same era.
R. W. Sharpe, Differential geometry: Cartan’s Generalization of Klein’s Erlangen Program
1997
Cited alongside, same era.
D. K. Wise, Symmetric space Cartan connections and gravity in three and four dimensions, SIGMA
Original
2009
Cited alongside, same era.
A. Shaukat and A. Waldron, Weyl’s gauge Invariance: conformal geometry, spinors, supersymmetry, and interactions, arXiv:0911.2477
Original
Cited in the paper.
S. Gielen and D. K. Wise, Spontaneous symmetry breaking for Hamiltonian gravity, arXiv:1111.7195
Original
Cited in the paper.
A. Randono, Gauge gravity: a forward-looking introduction, arXiv:1010.5822
Original
Cited in the paper.

Then

R. Percacci, Gravity from a particle physicist’s perspective, PoS ISFTG
Original
2009
Later among the works it cites.
D. K. Wise, MacDowell–Mansouri gravity and Cartan geometry, Class. Quant. Grav
2010
Later among the works it cites.

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