Loops 13
I will describe a very large class of gauge theories that do not use any external structure such as e.g. a spacetime metric in their construction. When the gauge group is taken to be SL(2) these theories describe interacting gravitons, with GR being just a particular member of a whole family of gravity theories. Taking larger gauge groups one obtains gravity coupled to various matter systems. In particular, I will show how gravity together with Yang-Mills gauge fields arise from one and the same diffeomorphism invariant gauge theory Lagrangian.
Several lines of evidence hint that quantum gravity at distances a bit larger than the Planck scale may become effectively two-dimensional. I will summarize the evidence for this "spontaneous dimensional reduction," and suggest a further argument based on the effect of vacuum fluctuations on light cones. If this description proves to be correct, it suggests an interesting relationship between small-scale quantum spacetime and the behavior of cosmologies near a spacelike singularity.