A Renormalizable 4-Dimensional Tensor Field Theory

By Joseph Ben Geloun, Vincent Rivasseau. 2011

209 citations recorded by the source corpus.

We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the $${\phi^6}$$ rather than of the $${\phi^4}$$ type, since two different $${\phi^6}$$-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent $${(\int \phi^2)^2}$$ term, which can be interpreted as the generation of a scalar matter field out of pure gravity.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b16a387abbe5f86053466046d904e34f2b1bc5f1

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Citations in the corpus

Random tensor models in the large N limit: Uncoloring the colored tensor models (2012, background): “We do not consider this second category of models further in this paper, except to recall that uncolored renormalizable models of this type have been found for rank 3 and rank 4 tensors [59, 60].”
O(N) Random Tensor Models (2015, background): “Many interesting results have been gathered for both colored or uncolored tensor models, including the characterization of next-to-leading order Feynman graphs in the large N expansion and the definition of a double-scaling limit [10–12], or universality results [13] proven with constructive…”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, background): “This gauge symmetry is a very important feature of the models considered in this paper, that will require significant modifications of the multi-scale analysis of [83].”
Universality for Random Tensors (2011, methodology): “The algorithm we present here has been introduced in [36].”