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 foam models obtained from a group field theory formalism. We propose an extension of the usual Barrett-Crane group field theory introducing an extra variable, thus working with five copies of the Lorentz group instead of four. This allows the definition of a new class of spin foam models with an explicit coupling between the (timelike) normals to the tetrahedra. We then focus on a specific model in which this coupling is parametrised by an additional real parameter that allows to tune its degree of locality. This model interpolates between the usual Barrett-Crane model and a flat BF-type one. Moreover, we define a further extension of the group field theory formalism in which the new coupling parameter enters as a new variable of the field. This modified action presents derivative terms that lead to modified classical equations of motion. Finally, we discuss how this new class of coupled models can be of help in the study of the renormalisation of spin foam models