Constructive Tensor Field Theory: The $T_3^4$ Model

Abstract

We build constructively the simplest tensor field theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse of the Laplacian on $U(1{)}^3$. This superrenormalizable tensor field theory has a power counting almost similar to ordinary ${\varphi }_2^4$. Our construction uses the multiscale loop vertex expansion (MLVE) recently introduced in the context of an analogous vector model. However to prove analyticity and Borel summability of this model requires new estimates on the intermediate field integration, which is now of matrix rather than of scalar type.

24 pages, 5 figures. Substantially improved version. Version v1 is correct but treats a model which is simplified at the level of the two point function. This version treats the full model, without any simplification

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Cited by in corpus (17)

• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Random Tensors and Quantum Gravity
• Why are tensor field theories asymptotically free?
• Constructive Tensor Field Theory
• Constructive tensor field theory: The $T_4^4$ model
• Loop Vertex Expansion for Higher Order Interactions
• The full Ward-Takahashi Identity for colored tensor models
• Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)
• Flowing in discrete gravity models and Ward identities: A review
• Note on the Intermediate Field Representation of Phi^2k Theory in Zero Dimension
• An $OSp$ extension of Canonical Tensor Model
• Intermediate Field Representation for Positive Matrix and Tensor Interactions
• Constructive expansion for quartic vector fields theories. I. Low dimensions
• Quartic Tensor Models
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint
• Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
• Can we make sense out of "Tensor Field Theory"?