6 research outputs found
The Immirzi Parameter as an Instanton Angle
The Barbero-Immirzi parameter is a one parameter quantization ambiguity
underpinning the loop approach to quantum gravity that bears tantalizing
similarities to the theta parameter of gauge theories such as Yang-Mills and
QCD. Despite the apparent semblance, the Barbero-Immirzi field has resisted a
direct topological interpretation along the same lines as the theta-parameter.
Here we offer such an interpretation. Our approach begins from the perspective
of Einstein-Cartan gravity as the symmetry broken phase of a de Sitter gauge
theory. From this angle, just as in ordinary gauge theories, a theta-term
emerges from the requirement that the vacuum is stable against quantum
mechanical tunneling. The Immirzi parameter is then identified as a combination
of Newton's constant, the cosmological constant, and the theta-parameter.Comment: 24 page
Gravity from a fermionic condensate of a gauge theory
The most prominent realization of gravity as a gauge theory similar to the
gauge theories of the standard model comes from enlarging the gauge group from
the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan
gravity the symmetry must be broken, which can be accomplished by known
quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle
physics and condensed matter systems, we propose that the symmetry can
naturally be broken by a homogenous and isotropic fermionic condensate of
ordinary spinors. We demonstrate that the condensate is compatible with the
Einstein-Cartan equations and can be imposed in a fully de Sitter invariant
manner. This lends support, and provides a physically realistic mechanism for
understanding gravity as a gauge theory with a spontaneously broken local de
Sitter symmetry.Comment: 16 page
The geometric role of symmetry breaking in gravity
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.Comment: 4 pages. Contribution written for proceedings of the conference
"Loops 11" (Madrid, May 2011