Holography for Tensor models

TL;DR

This paper investigates the holographic duals of tensor models through collective field theory, revealing matrix-like subsectors with extra dimensions and analyzing finite N effects and non-perturbative phenomena.

Contribution

It introduces a collective field theory framework for tensor models and distinguishes between sectors that develop extra holographic dimensions and those that do not.

Findings

Matrix-like subsectors develop an extra holographic dimension.

Melonic large N limits do not exhibit an extra dimension.

Finite N physics and non-perturbative effects are analyzed.

Abstract

In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrix like subsectors that develop an extra holographic dimension. In contrast to this, we argue that melonic large $N$ limits do not develop an extra dimension. The finite $N$ physics of the model is also developed and non-perturbative effects in the $1/N$ expansion are exhibited.