Phase Transition in Tensor Models

Abstract

Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a $1/N$ expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in $1/N$ (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.

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Cited by in corpus (11)

• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Functional Renormalisation Group analysis of a Tensorial Group Field Theory on ${\mathbb{R}}^3$
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Large $N$ limit of irreducible tensor models: $O(N)$ rank-$3$ tensors with mixed permutation symmetry
• Symmetry breaking in tensor models
• Phase transitions in group field theory: The Landau perspective
• Revisited functional renormalization group approach for random matrices in the large-$N$ limit
• Inequivalent coherent state representations in group field theory
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Flowing in discrete gravity models and Ward identities: A review
• An $OSp$ extension of Canonical Tensor Model