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Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions

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arxiv 1303.6772 v3 pith:AVG2CRDO submitted 2013-03-27 hep-th gr-qc

Sylvain Carrozza , Daniele Oriti , Vincent Rivasseau This is my paper · ORCID
classification hep-thgr-qc
keywords dimensionsrenormalizabletensorialthreefieldgroupjustmelonic
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We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.

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