  Controlling the continuum limit and extracting effective gravitational
physics are shared challenges for quantum gravity approaches based on quantum
discrete structures. The description of quantum gravity in terms of tensorial
group field theory (TGFT) has recently led to much progress in its application
to phenomenology, in particular cosmology. This application relies on the
assumption of a phase transition to a nontrivial vacuum (condensate) state
describable by mean-field theory, an assumption that is difficult to
corroborate by a full renormalization group flow analysis due to the complexity
of the relevant TGFT models. Here we demonstrate that this assumption is
justified due to the specific ingredients of realistic quantum geometric TGFT
models: combinatorially non-local interactions, matter degrees of freedom and
Lorentz group data together with the encoding of micro-causality. This greatly
strengthens the evidence for the existence of a meaningful continuum
gravitational regime in group-field and spin-foam quantum gravity, the
phenomenology of which is amenable to explicit computations in a mean-field
approximation.
