On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review

Abstract

When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'. In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.

12 pages; v2: references added

References in corpus (57)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Local BRST cohomology in gauge theories
• A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results
• The IR/UV Connection in the Non-Commutative Gauge Theories
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• On the unitarity problem in space/time noncommutative theories
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Comments on Noncommutative Perturbative Dynamics
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Vanishing of Beta Function of Non Commutative ${\Phi }_4^4$ Theory to all orders
• Comments on Perturbative Dynamics of Non-Commutative Yang-Mills Theory
• Noncommutative Geometry and the standard model with neutrino mixing
• Noncommutative Induced Gauge Theory
• The β-function in duality-covariant noncommutative ϕ^4-theory
• Renormalization of noncommutative phi 4-theory by multi-scale analysis
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• Noncommutative SO(n) and Sp(n) Gauge Theories
• A translation-invariant renormalizable non-commutative scalar model
• One Loop Renormalizability of Supersymmetric Yang-Mills Theories on Noncommutative Two-Torus
• Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
• Noncommutative Gauge Field Theories: A No-Go Theorem
• Induced Gauge Theory on a Noncommutative Space
• A Note on Superfields and Noncommutative Geometry
• Soft breaking of BRST invariance for introducing non-perturbative infrared effects in a local and renormalizable way
• Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map
• Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
• A Consistent Noncommutative Field Theory: the Wess-Zumino Model
• Time-ordered Perturbation Theory on Noncommutative Spacetime II: Unitarity
• Renormalizability of noncommutative SU(N) gauge theory
• Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
• Translation-invariant models for non-commutative gauge fields
• One-Loop Calculations for a Translation Invariant Non-Commutative Gauge Model
• Noncommutative $\mathcal{N}=1,2$ super U(N) Yang-Mills: UV/IR mixing and effective action results at one loop
• Restrictions on Gauge Groups in Noncommutative Gauge Theory
• Space/time noncommutative field theories and causality
• Towards a consistent noncommutative supersymmetric Yang-Mills theory: superfield covariant analysis
• Non-Commutative U(1) Gauge Theory on R**4 with Oscillator Term and BRST Symmetry
• Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories
• Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models
• A Renormalized Supersymmetry in the Topological Yang-Mills Field Theory
• Time ordered perturbation theory for non-local interactions; applications to NCQFT
• Duality covariant quantum field theory on noncommutative Minkowski space
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• Quantum Corrections for Translation-Invariant Renormalizable Non-Commutative Phi^4 Theory
• Descent equations of Yang--Mills anomalies in noncommutative geometry
• Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections
• Improved Localization of a Renormalizable Non-Commutative Translation Invariant U(1) Gauge Model
• One Loop Renormalization of Spontaneously Broken U(2) Gauge Theory on Noncommutative Spacetime
• Gauge Independence of IR singularities in Non-Commutative QFT - and Interpolating Gauges
• One-loop $\beta$ functions of a translation-invariant renormalizable noncommutative scalar model
• Renormalization of Spontaneaously Broken SU(2) Yang-Mills Theory with Flow Equations
• Nilpotent noncommutativity and renormalization
• IR-Singularities in Noncommutative Perturbative Dynamics?
• Space-time noncommutativity with a bifermionic parameter

Cited by in corpus (29)

• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Quantum gauge theories on noncommutative 3-d space
• Gauge theories on quantum spaces
• Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Gauge theories on $\kappa$-Minkowski spaces: Twist and modular operators
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Gauge Theories on Deformed Spaces
• A New Approach to Non-Commutative U(N) Gauge Fields
• Closed star product on noncommutative ${\mathbb{R}}^3$ and scalar field dynamics
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Twisted BRST symmetry in gauge theories on $\kappa$-Minkowski
• Involutive representations of coordinate algebras and quantum spaces
• Gauge fields on noncommutative geometries with curvature
• On Poisson Electrodynamics With Charged Fields
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• Aspects of perturbative quantum field theory on non-commutative spaces
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• Translation-Invariant Noncommutative Renormalization
• One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
• Strong Field, Noncommutative QED
• Perturbative effective action for the photon in noncommutative QED${}_2$ and exactness of the Schwinger mass
• One-loop $\beta$ function of noncommutative scalar $QE{D}_4$
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• Gauge Fields on Non-Commutative Spaces and Renormalization
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories