Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space

Abstract

In this paper we provide a new proof that the Grosse-Wulkenhaar non-commutative scalar Phi^4_4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).

32 pages, v2: correction of lemmas 3.1 and 3.2 with no consequence on the main result

References in corpus (12)

• String Theory and Noncommutative Geometry
• Noncommutative Field Theory
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Power-counting theorem for non-local matrix models and renormalisation
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Convergence Theorem for Non-commutative Feynman Graphs and Renormalization
• Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions

Cited by in corpus (60)

• Colored Tensor Models - a Review
• The complete 1/N expansion of colored tensor models in arbitrary dimension
• Colored Group Field Theory
• 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
• Group field theory renormalization - the 3d case: power counting of divergences
• Noncommutative Induced Gauge Theory
• Topological Graph Polynomials in Colored Group Field Theory
• A translation-invariant renormalizable non-commutative scalar model
• Induced Gauge Theory on a Noncommutative Space
• Lost in Translation: Topological Singularities in Group Field Theory
• Invitation to Random Tensors
• Vacuum configurations for renormalizable non-commutative scalar models
• Two and Three Loops Beta Function of Non Commutative ${\Phi }_4^4$ Theory
• Constructive Matrix Theory
• Parametric Representation of Noncommutative Field Theory
• Closed equations of the two-point functions for tensorial group field theory
• On the vacuum states for noncommutative gauge theory
• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Commutative limit of a renormalizable noncommutative model
• Overview of the parametric representation of renormalizable non-commutative field theory
• Parametric representation of "critical" noncommutative QFT models
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Tree Quantum Field Theory
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Duality covariant quantum field theory on noncommutative Minkowski space
• Noncommutative Induced Gauge Theories on Moyal Spaces
• One-loop Beta Functions for the Orientable Non-commutative Gross-Neveu Model
• Vanishing beta function for Grosse-Wulkenhaar model in a magnetic field
• Functional Renormalization of Noncommutative Scalar Field Theory
• Symmetries of noncommutative scalar field theory
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
• Spacetime and deformations of special relativistic kinematics
• Wilsonian Renormalization of Noncommutative Scalar Field Theory
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• Noncommutative Thermofield Dynamics
• Gauge fields on noncommutative geometries with curvature
• On the Renormalization of Non-Commutative Field Theories
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• Lehmann-Symanzik-Zimmermann S-Matrix elements on the Moyal Plane
• On the Effective Action of Noncommutative Yang-Mills Theory
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Propagators and Matrix Basis on Noncommutative Minkowski Space
• The fate of the Wilson-Fisher fixed point in non-commutative ϕ^4
• High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing
• Color Grosse-Wulkenhaar models: One-loop $\beta$-functions
• Renormalization of the commutative scalar theory with harmonic term to all orders
• Spinors on a curved noncommutative space: coupling to torsion and the Gross-Neveu model
• Effective Field Theory of a Locally Noncommutative Space-Time and Extra Dimensions
• Energy momentum tensor for translation invariant renormalizable noncommutative field theory
• Wilson RG of Noncommutative ${\Phi }_4^4$
• A numerical approach to harmonic non-commutative spectral field theory
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
• Vulcanized Vortex
• Exorcizing the Landau Ghost in Non Commutative Quantum Field Theory
• Non-commutative geometry and exactly solvable systems