Parametric representation of "critical" noncommutative QFT models

Abstract

We extend the parametric representation of renormalizable non commutative quantum field theories to a class of theories which we call "critical", because their power counting is definitely more difficult to obtain. This class of theories is important since it includes gauge theories, which should be relevant for the quantum Hall effect.

30 pages, 12 figures

References in corpus (13)

• 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
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Power-counting theorem for non-local matrix models and renormalisation
• Renormalization of Non-Commutative Phi^4_4 Field Theory in x Space
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Quantum Hall Physics = Noncommutative Field Theory
• Quantum Hall states on the cylinder as unitary matrix Chern-Simons theory
• Parametric Representation of Noncommutative Field Theory
• Renormalization of the Orientable Non-commutative Gross-Neveu Model
• Propagators for Noncommutative Field Theories

Cited by in corpus (13)

• Topological Graph Polynomials in Colored Group Field Theory
• Linearized Group Field Theory and Power Counting Theorems
• A translation-invariant renormalizable non-commutative scalar model
• Multi-orientable Group Field Theory
• Hopf algebra of non-commutative field theory
• Generalization of the Bollobás-Riordan polynomial for tensor graphs
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Commutative limit of a renormalizable noncommutative model
• Parametric representation of a translation-invariant renormalizable noncommutative model
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Tree Quantum Field Theory
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories