Phase Transition in Tensor Models

TL;DR

This paper studies tensor models, showing that their continuum limit corresponds to a phase transition in the associated field theory, extending the understanding of dynamical triangulations in higher dimensions.

Contribution

It introduces an explicit field theory formulation for tensor models around a vacuum state, revealing the phase transition associated with the continuum limit.

Findings

Identifies the critical regime as a phase transition in the fluctuation field

Rewrites tensor models as a field theory using the intermediate field representation

Connects the continuum limit in dynamical triangulations to a phase transition

Abstract

Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in $1/N$ (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.