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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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Cited by 2 Pith papers

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  1. Stochastic dynamics for group field theories II: Methods for nonequilibrium renormalization group

    hep-th 2025-09 conditional novelty 5.0 of 10

    Extending a stochastic renormalization-group method for tensor group field theories to non-equilibrium, this paper finds that fluctuation-dissipation-violating couplings become large near finite-scale singularities, i...

  2. Ward-constrained melonic renormalization group flow for the rank-four $\phi^6$ tensorial group field theory

    hep-th 2019-08 reject novelty 4.0 of 10

    For the rank-4 φ6 tensorial group field theory, the authors derive a Ward-constrained renormalization group flow and report a nontrivial fixed point, but the fixed point's reported values violate their own consistency...

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