Quantum Gravity

I comment on rather significant recent developments that are relevant for proposals I had presented in previous PI seminars. The Fermi/GLAST space telescope has reported observations that would naturally fit previous formalizations of Planck-scale-induced in-vacuo dispersion (but also quite a few other things). And the unexplained excess noise found at the GEO600 interferometer is just of the type that had been previously described in terms of phenomenological models of spacetime foam (but may well be caused by quite a few other things). On the pure-theory side I can finally keep my promise to show that spacetime noncommutativity is a valuable tool of exploration of nonclassicality of spacetime, allowing the derivation of discretized spectra of distance, area, volume, and also providing a completely new overall geometric picture, in which amusingly the number Pi looses some of its privileges.

Quantum graphity is a background independent condensed matter model for emergent locality, spatial geometry and matter in quantum gravity. The states of the system are given by bosonic degrees of freedom on a dynamical graph on N vertices. At high energy, the graph is the complete graph on N vertices and the physics is invariant under the full symmetric group acting on the vertices and highly non-local. The ground state dynamically breaks the permutation symmetry to translations and rotations. In this phase the system is ordered, low-dimensional and local. The model gives rise to an emergent U(1) gauge theory in the ground state by the string-net condensation mechanism of Levin and Wen. In addition, in such a model, observable effects of emergent locality such as its imprint on the CMB can be studied. Finding the right dynamics for the desired ground state is ongoing work and I will review some of the basic results with an emphasis on the use of methods from quantum information theory such as topological order and the use of the Lieb-Robinson bounds to find the speed of light in the system.

We derive geometric correlation functions in the new spinfoam model with coherent states techniques, making connection with quantum Regge calculus and perturbative quantum gravity. In particular we recover the expected scaling with distance for all components of the propagator. We expect the same technique to be well-suited for other spinfoam models.