Constructive tensor field theory: The $T_4^4$ model

Abstract

We continue our constructive study of tensor field theory through the next natural model, namely the rank four tensor theory with quartic melonic interactions and propagator inverse of the Laplacian on $U(1{)}^4$. This superrenormalizable tensor field theory has a power counting quite similar to ordinary ${\varphi }_3^4$. We control the model via a multiscale loop vertex expansion which has to be pushed quite beyond the one of the $T_3^4$ model and we establish its Borel summability in the coupling constant. This paper is also a step to prepare the constructive treatment of just renormalizable models, such as the $T_5^4$ model with quartic melonic interactions.

78 pages, 21 figures, 8 tables, minor modifications

References in corpus (15)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• The 1/N expansion of colored tensor models
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• The complete $1/N$ expansion of a SYK--like tensor model
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Scaling behaviour of three-dimensional group field theory
• Constructive ${\varphi }^4$ field theory without tears
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Quenched equals annealed at leading order in the colored SYK model
• Enhancing non-melonic triangulations: A tensor model mixing melonic and planar maps
• Progress in solving a noncommutative quantum field theory in four dimensions
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Loop Vertex Expansion for Higher Order Interactions

Cited by in corpus (11)

• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Flowing in discrete gravity models and Ward identities: A review
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Complete Solution of a Gauged Tensor Model
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Tensor Field Theories: Renormalization and Random Geometry
• Constructive expansion for quartic vector fields theories. I. Low dimensions
• Graph calculus and the disconnected-boundary Schwinger-Dyson equations of quartic tensor field theories
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• Melonic large $N$ limit of $5$-index irreducible random tensors
• Can we make sense out of "Tensor Field Theory"?