The Plebanski sectors of the EPRL vertex

TL;DR

This paper clarifies the role of Plebanski sectors in spin-foam models of quantum gravity, revealing that current constraints mix sectors and cause extra terms in the asymptotic behavior of the EPRL vertex.

Contribution

It provides a new interpretation of the linearized simplicity constraints, showing they do not restrict to a single Plebanski sector, explaining additional terms in the EPRL vertex asymptotics.

Findings

Three Plebanski sectors are mixed by the constraints.

The extra asymptotic terms are due to sector mixing.

This explanation differs from previous interpretations.

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.