Exact solution of matricial ${\Phi }_2^3$ quantum field theory

Abstract

We apply a recently developed method to exactly solve the ${\Phi }^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large-$\mathcal{N}$ limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the ${\Phi }^3$ coupling constant, although bounds on individual graphs justify only Borel summability. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

30 pages, LaTeX. v2: some formulae generalised to avoid duplication in arXiv:1612.07584

References in corpus (5)

• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Progress in solving a noncommutative quantum field theory in four dimensions
• Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity
• Solvable limits of a 4D noncommutative QFT
• The ${\Phi }_4^3$ and ${\Phi }_6^3$ matricial QFT models have reflection positive two-point function

Cited by in corpus (9)

• Ultraviolet-complete quantum field theories with fractional operators
• Solution of all quartic matrix models
• Lambert-W solves the noncommutative ${\Phi }^4$-model
• A Laplacian to compute intersection numbers on ${\bar{\mathcal{M}}}_{g,n}$ and correlation functions in NCQFT
• Large-$d$ behavior of the Feynman amplitudes for a just-renormalizable tensorial group field theory
• Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme
• Noncommutative 3-colour scalar quantum field theory model in 2D
• Blobbed topological recursion from extended loop equations
• Exact Solutions v.s. Perturbative Calculations of Finite ${\Phi }^3$-${\Phi }^4$ Hybrid-Matrix-Model