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.

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Cited by in corpus (30)

• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Double Scaling in Tensor Models with a Quartic Interaction
• The Tensor Track, III
• The 1/N Expansion of Tensor Models Beyond Perturbation Theory
• Revisiting random tensor models at large N via the Schwinger-Dyson equations
• Some classes of renormalizable tensor models
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Invitation to Random Tensors
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Group field theories for all loop quantum gravity
• Towards a double-scaling limit for tensor models: probing sub-dominant orders
• Melonic phase transition in group field theory
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Two and four-loop $\beta$-functions of rank 4 renormalizable tensor field theories
• Multicritical tensor models and hard dimers on spherical random lattices
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Addendum to "A Renormalizable 4-Dimensional Tensor Field Theory"
• Canonical tensor models with local time
• Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
• Uniqueness of canonical tensor model with local time
• Phase diagram and fixed points of tensorial Gross-Neveu models in three dimensions
• A Renormalizable 4-Dimensional Tensor Field Theory
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Renormalizable Models in Rank $d\ge 2$ Tensorial Group Field Theory
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Minisuperspace computation of the Mabuchi spectrum
• Tensor models from the viewpoint of matrix models: the case of the Gaussian distribution
• Tensor Field Theories: Renormalization and Random Geometry