  We consider the special case of Random Tensor Networks (RTN) endowed with
gauge symmetry constraints on each tensor. We compute the R\`enyi entropy for
such states and recover the Ryu-Takayanagi (RT) formula in the large bond
regime. The result provides first of all an interesting new extension of the
existing derivations of the RT formula for RTNs. Moreover, this extension of
the RTN formalism brings it in direct relation with (tensorial) group field
theories (and spin networks), and thus provides new tools for realizing the
tensor network/geometry duality in the context of background independent
quantum gravity, and for importing quantum gravity tools in tensor network
research.
