REGGE GRAVITY FROM SPINFOAMS

We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.