3D tensor field theory: renormalization and one-loop \(\beta \)-functions. (English) Zbl 1272.83028
Summary: We prove that the rank 3 analogue of the tensor model defined in [the first author and V. Rivasseau, Commun. Math. Phys. 318, No. 1, 69–109 (2013; Zbl 1261.83016); addendum ibid. 322, No. 3, 957–965 (2013; Zbl 1272.83027)] is renormalizable at all orders of perturbation. The proof is given in the momentum space. The one-loop \(\gamma \)- and \(\beta \)-functions of the model are also determined. We find that the model with a unique coupling constant for all interactions and a unique wave-function renormalization is asymptotically free in the UV.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81S40 | Path integrals in quantum mechanics |
Keywords:
3D tensor field theory; renormalization; wave-function renormalization; asymptotically freeReferences:
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