A Renormalizable SYK-type Tensor Field Theory

TL;DR

This paper introduces a renormalizable tensor field theory inspired by SYK models, providing a familiar momentum-space interpretation and proving its renormalizability through multiscale analysis, bridging holographic tensor models and condensed matter physics.

Contribution

It presents a simple, renormalizable tensor field theory with a momentum-space interpretation, connecting SYK models to conventional condensed matter frameworks.

Findings

Proves the model is renormalizable to all orders in perturbation theory.

Provides a momentum-space interpretation of SYK/CTKT models.

Bridges holographic tensor models with condensed matter physics.

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 multiscale analysis we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.