Renormalization of a \(\mathrm{SU}(2)\) tensorial group field theory in three dimensions
The renormalizability of a \(\mathrm{SU}(2)\) tensorial group field theory in three dimensions is shown. This is part of the program to construct a (non-abelian) tensorial group field theory in four dimensions, which is hoped to describe quantum gravity. The analysis is based on concepts introduced in a previous work of the same authors [Commun. Math. Phys. 327, No. 2, 603--641 (2014; Zbl 1291.83102)], in particular the notion of face-connectedness of a graph. The proof of renormalizability uses multi-scale techniques.
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