Published August 1, 2013
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Some classes of renormalizable tensor models

  • 1. Perimeter Institute for Theoretical Physics 1 , 31 Caroline Str. N, ON N2L 2Y5, Waterloo, Ontario, Canada
  • 2. Perimeter Institute for Theoretical Physics
  • 3. International Chair in Mathematical Physics and Applications 2 , ICMPA-UNESCO Chair, 072BP50 Cotonou, Republic of Benin
  • 4. Laboratoire de Physique 3 , ENS Lyon, CNRS-UMR 5672, 46 Allée d'Italie, Lyon 69007, France

Description

We identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property. Mainly, a version of the rank 3 tensor model as defined by Ben Geloun and Samary [Ann. Henri Poincare 14, 1599 (2013); e-print arXiv:1201.0176 [hep-th]]10.1007/s00023-012-0225-5 and the Grosse-Wulkenhaar model in 4D and 2D generate three different classes of renormalizable models. The proof of the renormalizability is fully performed for the first reduced model. The same procedure can be applied for the remaining cases. Interestingly, we find that, due to the peculiar behavior of anisotropic wave function renormalizations, the rank 3 tensor model reduced to a matrix model generates a simple super-renormalizable vector model.
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