  In the context of quantum gravity, group field theories are field theories
that generate spinfoam amplitudes as Feynman diagrams. They can be understood
as generalizations of the matrix models used for 2d quantum gravity. In
particular Boulatov's theory reproduces the amplitudes of the Ponzano-Regge
spinfoam model for 3d quantum gravity. Motivated by recent works on field
theories on non-commutative flat spaces, we show that Boulatov's theory (and
its colored version) is actually invariant under a global deformed Poincare
symmetry. This allows to define a notion of flat/excited geometry states when
considering scalar perturbations around classical solutions of the group field
equations of motion. As a side-result, our analysis seems to point out that the
notion of braiding of group field theories should be a key feature to study
further in this context.
