Coupling of spacetime atoms in 4D spin foam models from group field theory

We study the issue of coupling among 4-simplices in the context of spin foammodels obtained from a group field theory formalism. We construct ageneralisation of the Barrett-Crane model in which an additional couplingbetween the normals to tetrahedra, as defined in different 4-simplices thatshare them, is present. This is realised through an extension of the usualfield over the group manifold to a five argument one. We define a specificmodel in which this coupling is parametrised by an additional real parameterthat allows to tune the degree of locality of the resulting model,interpolating between the usual Barrett-Crane model and a flat BF-type one.Moreover, we define a further extension of the group field theory formalism inwhich the coupling parameter enters as a new variable of the field, and theaction presents derivative terms that lead to modified classical equations ofmotion. Finally, we discuss the issue of renormalisation of spin foam models,and how the new coupled model can be of help regarding this.Comment: RevTeX, 18 pages, no figure