  Group field theories are a generalization of matrix models which provide both
a second quantized reformulation of loop quantum gravity as well as generating
functions for spin foam models. While states in canonical loop quantum gravity,
in the traditional continuum setting, are based on graphs with vertices of
arbitrary valence, group field theories have been defined so far in a
simplicial setting such that states have support only on graphs of fixed
valency. This has led to the question whether group field theory can indeed
cover the whole state space of loop quantum gravity. In this contribution based
on [1] I present two new classes of group field theories which satisfy this
objective: i) a straightforward, but rather formal generalization to multiple
fields, one for each valency and ii) a simplicial group field theory which
effectively covers the larger state space through a dual weighting, a technique
common in matrix and tensor models. To this end I will further discuss in some
detail the combinatorial structure of the complexes generated by the group
field theory partition function. The new group field theories do not only
strengthen the links between the mentioned quantum gravity approaches but,
broadening the theory space of group field theories, they might also prove
useful in the investigation of renormalizability.
