Double scaling limit in arbitrary dimensions: A toy model

Abstract

Colored tensor models generalize matrix models in arbitrary dimensions, yielding a statistical theory of random higher-dimensional topological spaces. They admit a $1/N$ expansion dominated by graphs of spherical topology. The simplest tensor model one can consider maps onto a rectangular matrix model with skewed scalings. We analyze this simplest toy model and show that it exhibits a family of multicritical points and a novel double scaling limit. We show in $D=3$ dimensions that only graphs representing spheres contribute in the double scaling limit and argue that similar results hold for any dimension.