The Plebanski sectors of the EPRL vertex

Abstract

Modern spin-foam models of four dimensional gravity are based on a discrete version of the $Spin(4)$ Plebanski formulation. Beyond what is already in the literature, we clarify the meaning of different Plebanski sectors in this classical discrete model. We show that the linearized simplicity constraints used in the EPRL and FK models are not sufficient to impose a restriction to a single Plebanski sector, but rather, three Plebanski sectors are mixed. We propose this as the reason for certain extra `undesired' terms in the asymptotics of the EPRL vertex analyzed by Barrett et al. This explanation for the extra terms is new and different from that sometimes offered in the spin-foam literature thus far.

17 pages

References in corpus (6)

• LQG vertex with finite Immirzi parameter
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Area-angle variables for general relativity
• Spin foam model from canonical quantization
• Spinfoams in the holomorphic representation

Cited by in corpus (15)

• Holonomy spin foam models: Asymptotic geometry of the partition function
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• A proposed proper EPRL vertex amplitude
• A spin-foam vertex amplitude with the correct semiclassical limit
• Linking covariant and canonical LQG II: Spin foam projector
• Divergences and Orientation in Spinfoams
• The Lorentzian proper vertex amplitude: Asymptotics
• The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Corrigendum: The Plebanski sectors of the EPRL vertex
• The kernel and the injectivity of the EPRL map
• Spinfoam cosmology with the proper vertex amplitude
• Spin foams
• Hessian and graviton propagator of the proper vertex
• Purely geometric path integral for spin foams