High Energy Theory Group Meeting: The geometry of spacetime in loop quantum gravity

Abstract:

The talk will consist of two parts. In the first part, I will introduce the audience to basic elements of the loop quantum gravity framework. General relativity can be formulated, using a particular choice of variables, in a way which resembles Yang-Mills theory with SU(2) as its gauge group. Familiar concepts and techniques from Yang-Mills theory can then be applied to gravity, and in particular, this enables the canonical quantization of gravity in a way which is background-independent and non-perturbative. After quantization, the quantum states of the gravitational field are described by graphs called spin networks, which are a generalization of Wilson loops. In the second part of the talk, I will present the results of my recent work with Laurent Freidel and Florian Girelli (to be published soon) showing that, in 2+1 spacetime dimensions, the phase space structure of classical spin networks corresponds to that of piecewise-flat geometries with vanishing torsion. Finally, I will comment about work in progress generalizing this result to the physically relevant case of 3+1 dimensions.