The 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 multi critical 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.