Tensor Models for Black Hole Probes

TL;DR

This paper generalizes tensor models related to the SYK model to include probe fields, maintaining maximal chaos and symmetry features, thus modeling black hole probes in a holographic context.

Contribution

Introduces a new class of tensor models with probe fields that preserve key black hole features like chaos and symmetry in the large N limit.

Findings

Probe fields exhibit maximal chaos similar to original models.

Probe primaries share the same dimensions as original primaries.

Dynamics of the original model remain unaffected by probes at large N.

Abstract

The infrared dynamics of the SYK model, as well as its associated tensor models, exhibit some of the non trivial features expected of a holographic dual of near extremal black holes. These include developing certain symmetries of the near horizon geometry and exhibiting maximal chaos. In this paper we present a generalization of these tensor models to include fields with fewer tensor indices and which can be thought of as describing probes in a black hole background. In large $N$ limit, dynamics of the original model remain unaffected by the probe fields and the four point functions of the probe fields exhibit maximal chaos, a non trivial feature expected of a black hole probe. Interestingly probe primaries have the same dimensions as primaries of the original fields.