The double scaling limit of the multi-orientable tensor model

¹ CPHT, UMR CNRS 7644, École Polytechnique, Univ. Paris-Saclay - 91128 Palaiseau cedex, France, EU
² Perimeter Institute for Theoretical Physics - 31 Caroline st. N, N2L 2Y5, Waterloo, ON, Canada
³ LIPN, UMR CNRS 7030, Univ. Paris 13, Sorbonne Paris Cité - 99 av. Clément, 93430 Villetaneuse, France, EU
⁴ H. Hulubei National Institute for Physics and Nuclear Physics - PO Box MG-6, 077125 Magurele, Romania, EU
⁵ Master ICFP, Département de Physique, ENS-PSL Research University - 24 rue Lhomond, 75005 Paris, France, EU

Received: 13 May 2015
Accepted: 20 July 2015

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.