Towards a double-scaling limit for tensor models: probing sub-dominant orders

Abstract

The definition of a double-scaling limit represents an important goal in the development of tensor models. We take the first steps towards this goal by extracting and analysing the next-to-leading order contributions, in the 1/N expansion, for the IID tensor models. We show that the radius of convergence of the NLO series coincides with that of the leading order melonic sector. Meanwhile, the value of the susceptibility exponent at NLO is 3/2, signaling a departure from the leading order behaviour. Both pieces of information provide clues for a non-trivial double-scaling limit, for which we put forward some precise conjecture.

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• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
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• Tensorial methods and renormalization in Group Field Theories
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Melonic phase transition in group field theory
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
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• Physical states in the canonical tensor model from the perspective of random tensor networks
• Conformality of $1/N$ corrections in SYK-like models
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• An $OSp$ extension of Canonical Tensor Model
• A Givental-like Formula and Bilinear Identities for Tensor Models
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• Multiple scaling limits of $\mathrm{U}(N{)}^2\times \mathrm{O}(D)$ multi-matrix models
• Tensor Models: extending the matrix models structures and methods
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model