The double scaling limit of the multi-orientable tensor model

TL;DR

This paper investigates the double scaling limit of the multi-orientable tensor model, revealing convergence properties and potential for a triple scaling limit, contrasting with matrix models.

Contribution

It proves the convergence of the double scaling series in tensor models and explores the behavior of correlation functions, suggesting a new triple scaling limit.

Findings

Double scaling series are convergent in tensor models.

Correlation functions are enhanced in the double scaling limit.

All correlation functions share a critical singularity.

Abstract

In this paper we study the double scaling limit of the multi-orientable tensor model. We prove that, contrary to the case of matrix models but similarly to the case of invariant tensor models, the double scaling series are convergent. We resum the double scaling series of the two point function and of the leading singular part of the four point function. We discuss the behavior of the leading singular part of arbitrary correlation functions. We show that the contribution of the four point function and of all the higher point functions are enhanced in the double scaling limit. We finally show that all the correlation functions exhibit a singularity at the same critical value of the double scaling parameter which, combined with the convergence of the double scaling series, suggest the existence of a triple scaling limit.