Lattice-regularized spinor quantum gravity

by Dmitri Diakonov (Petersburg Nuclear Physics Institute)

Monday 17 Oct 2011, 14:00 → 15:00 Europe/Zurich

Salle 727 BSP Cubotron (EPFL)

If Cartan formulation of General Relativity is used, as the presence of fermions seems to force us to do, none of the possible diffeomorphism-invariant terms in the action are sign-definite. This prevents one from defining quantum gravity in a nonperturbative sense when all quantum fluctuations of the metrics and of the connection, including sign-changing ones are in principle allowed. A way out is to use a composite frame field, built as a bilinear "current" of more fundamental fermion (spinor) fields. Path integrals over Grassmannian variables are well defined for whatever sign of the fermion action. Thus in the ultraviolet limit quantum gravity possesses only spinor and gauge field degrees of freedom, like in the Standard Model. The theory can be easily regularized by putting it on a space lattice. It is explicitly invariant under local Lorentz transformations and, in the continuum limit, under diffeomorphisms. It is a theory that is wellbehaved at small distances, and quantum fluctuations are well defined. I discuss how to check if Newton's law is reproduced in the infrared limit. Also, this formulation of quantum gravity allows its unification with the Standard Model, and that will be also briefly discussed.