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A Renormalizable SYK-Type Tensor Field Theory

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Abstract

In this paper we introduce a simple field theoretic version of the Carrozza–Tanasa–Klebanov–Tarnopolsky (CTKT) “uncolored” holographic tensor model. It gives a more familiar interpretation to the previously abstract modes of the SYK or CTKT models in terms of momenta. We choose for the tensor propagator the usual Fermionic propagator of condensed matter, with a spherical Fermi surface, but keep the CTKT interactions. Hence, our field theory can also be considered as an ordinary condensed matter model with a non-local and non-rotational invariant interaction. Using a multi-scale analysis, we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.

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Acknowledgements

V. Rivasseau thanks N. Delporte, F. Ferrari, R. Gurau and G. Valette for useful discussions.

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Authors and Affiliations

  1. LIPN UMR CNRS 7030 Institut Galilée, Université Paris 13 Sorbonne Paris Cité, 99, avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Joseph Ben Geloun

  2. International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, 072Bp50, Cotonou, Benin

    Joseph Ben Geloun

  3. Laboratoire de Physique Théorique CNRS UMR 8627, Université Paris XI, 91405, Orsay Cedex, France

    Vincent Rivasseau

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  1. Joseph Ben Geloun
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Correspondence to Vincent Rivasseau.

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Communicated by Abdelmalek Abdesselam.

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Ben Geloun, J., Rivasseau, V. A Renormalizable SYK-Type Tensor Field Theory. Ann. Henri Poincaré 19, 3357–3395 (2018). https://doi.org/10.1007/s00023-018-0712-4

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