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Starting from Plebanski formulation of gravity as a constrained BF theory wepropose a new spin foam model for 4d Riemannian quantum gravity thatgeneralises the well-known Barrett-Crane model and resolves the inherent to itultra-locality problem. The BF formulation of 4d gravity possesses two sectors:gravitational and topological ones. The model presented here is shown to give aquantization of the gravitational sector, and is dual to the recently proposedspin foam model of Engle et al. which, we show, corresponds to the topologicalsector. Our methods allow us to introduce the Immirzi parameter into theframework of spin foam quantisation. We generalize some of our considerationsto the Lorentzian setting and obtain a new spin foam model in that context aswell.

A New Spin Foam Model for 4d Gravity