47 research outputs found
Gauge Gravity: a forward-looking introduction
This article is a review of modern approaches to gravity that treat the
gravitational interaction as a type of gauge theory. The purpose of the article
is twofold. First, it is written in a colloquial style and is intended to be a
pedagogical introduction to the gauge approach to gravity. I begin with a
review of the Einstein-Cartan formulation of gravity, move on to the
Macdowell-Mansouri approach, then show how gravity can be viewed as the
symmetry broken phase of an (A)dS-gauge theory. This covers roughly the first
half of the article. Armed with these tools, the remainder of the article is
geared toward new insights and new lines of research that can be gained by
viewing gravity from this perspective. Drawing from familiar concepts from the
symmetry broken gauge theories of the standard model, we show how the
topological structure of the gauge group allows for an infinite class of new
solutions to the Einstein-Cartan field equations that can be thought of as
degenerate ground states of the theory. We argue that quantum mechanical
tunneling allows for transitions between the degenerate vacua. Generalizing the
tunneling process from a topological phase of the gauge theory to an arbitrary
geometry leads to a modern reformulation of the Hartle-Hawking "no boundary"
proposal.Comment: 62 pages, 8 figure
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
In Search of Quantum de Sitter Space: Generalizing the Kodama State
The Kodama state is unique in being an exact solution to all the constraints
of quantum gravity that also has a well defined semi-classical interpretation
as the quantum version of a classical spacetime, namely de Sitter or anti-de
sitter space. Despite this, the state fails to pass some of the key tests of a
physically realistic quantum state. In an attempt to resolve this problem, we
track down the root of the problem to a choice for a particular parameter: the
Immirzi parameter. The Kodama state takes this parameter to be complex, whereas
modern formulations of canonical quantum gravity require that the parameter is
real. We generalize the Kodama state to real values of the Immirzi parameter,
and find that the generalization opens up a large Hilbert space of states, one
of which can be directly interpreted as particular slicing of de Sitter space.
We then show that these states resolve, or are expected to resolve many of the
problems associated with the original version of the Kodama state. In order to
resolve the interpretation of the multitude of states, we develop a new model
of covariant classical and quantum gravity where the full Lorentz group is
retained as a local symmetry group, and the canonical evolution generated by
the constraints has a close relation to a larger group: the de Sitter group.
This formalism gives strong evidence that the multitude of generalized Kodama
states can be unified into a single quantum state that is quantum de Sitter
space.Comment: Ph.D. dissertation, University of Texas at Austin. 150 pages tota
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