A Renormalizable 4Dimensional Tensor Field Theory
Abstract
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 spacetime in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are fourstranded 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 logdivergent, 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 logdivergent $(\int \phi^2)^2$ term, which can be interpreted as the generation of a scalar matter field out of pure gravity.
 Publication:

arXiv eprints
 Pub Date:
 November 2011
 arXiv:
 arXiv:1111.4997
 Bibcode:
 2011arXiv1111.4997B
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 44 pages, 11 figures, typos corrected, figures added, improved version