Loop Vertex Expansion for Higher Order Interactions

Abstract

This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the $(\bar{\varphi }\varphi {)}^p$ field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.

16 pages, 2 figures, V2, minor modifications

References in corpus (6)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• The 1/N expansion of colored tensor models
• The complete $1/N$ expansion of a SYK--like tensor model
• Quantum Chaos and Holographic Tensor Models
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• Constructive ${\varphi }^4$ field theory without tears

Cited by in corpus (8)

• Contrasting SYK-like Models
• Constructive tensor field theory: The $T_4^4$ model
• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Schwinger-Dyson and loop equations for a product of square Ginibre random matrices
• Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass
• Constructive expansion for quartic vector fields theories. I. Low dimensions
• The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group
• Can we make sense out of "Tensor Field Theory"?