Séminaires sur les aspects théoriques et expérimentaux de la gravitation
# Discrete Wheeler DeWitt equation

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Amphithéâtre Léon Motchane (Institut des Hautes Etudes Scientifiques)
### Amphithéâtre Léon Motchane

#### Institut des Hautes Etudes Scientifiques

Bois-Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. For this talk, first, the case of 2+1 dimensions is presented. The wavefunction solutions only depend on the geometric quantities indicating preservation of diffeomorphism. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in G located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be nu=6/11. The results obtained lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class. I then discuss some results in 3+1 dimensions. Investigations of the vacuum wave functional further indicate that for weak enough coupling, G < Gc, a pathological ground state with no continuum limit appears, where configurations with small curvature have vanishingly small probability.

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