We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that ...

The action of general relativity proposed by Capovilla, Jacobson and Dell is written in terms of SO(3) gauge fields and gives Ashtekar's constraints for Einstein gravity. However, it does not depend on the space-time metric nor its signature explicitly. We discuss how the space-time metric is introduced from algebraic relations of the constraints and the Hamiltonian by focusing our attention on...

A Lorentzian manifold is defined here as a smooth pseudoRiemannian manifold with a metric tensor of signature (2n + 1, 1). A Robinson manifold is a Lorentzian manifold M of dimension > 4 with a subbundle N of the complexification of TM such that the fibers of N → M are maximal totally null (isotropic) and [SecN,SecN ] ⊂ SecN . Robinson manifolds are close analogs of the proper Riemannian, Hermi...

The formalism of Greensite for treating the spacetime signature as a dynamical degree of freedom induced by quantum elds is considered, for spacetimes with nontrivial topology of the kind R 1 T, for varying D. It is shown that a dynamical origin for the Lorentzian signature is possible in the ve-dimensional space R T with small torus radius (periodic boundary conditions), as well as in four-dim...