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On spinfoam models in large spin regime. (English) Zbl 1287.83022

Summary: We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters and the so-called, almost analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as \(J_{f} = {\lambda}{j_{f}}\), where \({\lambda}\) is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows that at least for the simplicial Lorentzian geometries (as spinfoam critical configurations), they contribute the leading order approximation of spinfoam amplitude only when their deficit angles satisfy \(\gamma\overset\circ\Theta_f\leqslant \lambda ^{-1/2}\,\mathrm{mod}\, 4\pi \mathbb {Z}\). Our analysis results in a curvature expansion of the semiclassical low energy effective action from the spinfoam model, where the UV modifications of Einstein gravity appear as subleading high-curvature corrections.

MSC:

83C45 Quantization of the gravitational field
83C60 Spinor and twistor methods in general relativity and gravitational theory; Newman-Penrose formalism
83C27 Lattice gravity, Regge calculus and other discrete methods in general relativity and gravitational theory
81T15 Perturbative methods of renormalization applied to problems in quantum field theory