This is a particular model in 3d quantum gravity
There is a similar reasoning in 3+1 d in
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Roberto De Pietri, Laurent Freidel, Kirill Krasnov, Carlo Rovelli, Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space, Nuclear Phys. B 574 (2000), no. 3, 785–806, arxiv/hep-th/9907154, MR2001f:83050, doi
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