Two papers that are part of this development came out just this past quarter (Jan-March 2015) and are on the "most important paper" Poll:
https://www.physicsforums.com/threa...rter-2015-mip-most-important-qg-paper.806409/
http://arxiv.org/abs/1503.07855
Loop quantum cosmology with self-dual variables
Edward Wilson-Ewing
(Submitted on 26 Mar 2015)
Using the
complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann universe coupled to a massless scalar field is studied. It is shown how the
reality conditions can be imposed in the quantum theory by choosing a particular measure for the inner product in the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well-defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomy-like operators, some of which are well-defined; these operators in turn are used in the definition of a Hamiltonian constraint operator where the scalar field can be used as a relational clock.
The resulting quantum dynamics are similar, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived, which provide a good approximation to the full quantum dynamics for sharply-peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects
resolve the big-bang and big-crunch singularities and replace them by a non-singular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.
10 pages
http://inspirehep.net/record/1356275
http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015)
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
8 pages
http://inspirehep.net/record/1356275
Carlip has an earlier paper on this same theme (developing the original self-dual Ashtekar variables in LQG, simply putting γ = i.)
http://arxiv.org/abs/1410.5763
A Note on Black Hole Entropy in Loop Quantum Gravity
S. Carlip
(Submitted on 21 Oct 2014 (
v1), last revised 26 Mar 2015 (this version, v3))
Several recent results have hinted that black hole thermodynamics in loop quantum gravity simplifies if one chooses an imaginary Barbero-Immirzi parameter γ=i. This suggests a connection with SL(2,ℂ) or SL(2,ℝ) conformal field theories at the "boundaries" formed by spin network edges intersecting the horizon. I present a bit of background regarding the relevant conformal field theories, along with some speculations about how they might be used to count black hole states. I show, in particular, that a set of unproven but plausible assumptions can lead to a boundary conformal field theory whose density of states matches the Bekenstein-Hawking entropy.
13 pages.
