The IR/UV Connection in the Non-Commutative Gauge Theories

Abstract

Quantum field theory on non-commutative spaces does not enjoy the usual ultraviolet-infrared decoupling that forms the basis for conventional renormalization. The high momentum contributions to loop integrations can lead to unfamiliar long distance behavior which can potentially undermine naive expectations for the IR behavior of the theory. These "anomalies" involve non-analytic behavior in the noncommutativity parameter Theta making the limit Theta goes to zero singular. In this paper we will analyze such effects in the one loop approximation to gauge theories on non-commutative space. We will see that contrary to expectations poles in Theta do occur and lead to large discrepancies between the expected and actual infrared behavior. We find that poles in Theta are absent in supersymmetric theories. The "anomalies" are generally still present, but only at the logarithmic level. A notable exception is non-commutative super Yang Mills theory with 16 real supercharges in which anomalous effects seem to be absent altogether.

17 pages, 7 figures, Appendix

References in corpus (1)

• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4

Cited by in corpus (334)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Modern tests of Lorentz invariance
• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Quantum Spacetime Phenomenology
• Space-Time Noncommutative Field Theories And Unitarity
• Noncommutative Solitons
• Planck-scale modified dispersion relations and Finsler geometry
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Comments on Noncommutative Perturbative Dynamics
• General Properties of Noncommutative Field Theories
• Signals for Non-Commutative Interactions at Linear Colliders
• Uncertainty Relation on World Crystal and its Applications to Micro Black Holes
• Review of the Phenomenology of Noncommutative Geometry
• Coproduct and star product in field theories on Lie-algebra non-commutative space-times
• Comments on Non-Commutative Phenomenology
• Emergent Gravity from Noncommutative Gauge Theory
• Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
• Noncommutative ${\Phi }^4$ Theory at Two Loops
• Noncommutative Induced Gauge Theory
• Scaling Limits of the Fuzzy Sphere at one Loop
• Noncommutative QED and Anomalous Dipole Moments
• Gauge-fixing independence of IR divergences in non-commutative U(1), perturbative tachyonic instabilities and supersymmetry
• The Search for Quantum Gravity Signals
• Improved limit on quantum-spacetime modifications of Lorentz symmetry from observations of gamma-ray blazars
• Chiral Gauge Anomalies on Noncommutative R^4
• Non-renormalizability of θ-expanded noncommutative QED
• Optical cavity tests of Lorentz invariance for the electron
• Quantum-Gravity Phenomenology: Status and Prospects
• Renormalization of noncommutative U(N) gauge theories
• Emergent Gravity and Noncommutative Branes from Yang-Mills Matrix Models
• Lorentz and CPT Invariance Violation In High-Energy Neutrinos
• UV/IR Mixing via Closed Strings and Tachyonic Instabilities
• The noncommutative harmonic oscillator in more than one dimensions
• The Meaning of Infrared Singularities in Noncommutative Gauge Theories
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Axial Anomaly in Noncommutative QED on R^4
• Shadow of a Charged Rotating Non-Commutative Black Hole
• Space-time quantum solves three experimental paradoxes
• Phase diagram and dispersion relation of the non-commutative λϕ^{4} model in d=3
• *-TREK: The One-Loop N=4 Noncommutative SYM Action
• Supersymmetric Noncommutative QED and Lorentz Violation
• Noncommutative geometry and physics: a review of selected recent results
• A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability
• Noncommutative Gauge Dynamics From The String Worldsheet
• Renormalizability of noncommutative SU(N) gauge theory
• On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review
• Imperfect fluids, Lorentz violations and Finsler Cosmology
• Quantum Gravity, Field Theory and Signatures of Noncommutative Spacetime
• The one-loop renormalization of the gauge sector in the noncommutative standard model
• Stretched Strings in Noncommutative Field Theory
• Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry
• Emergent Gravity, Matrix Models and UV/IR Mixing
• Fractional and noncommutative spacetimes
• Hermitian Analyticity, IR/UV Mixing and Unitarity of Noncommutative Field Theories
• Noncommutative field theory on ${\mathbb{R}}_{\lambda }^3$
• Quantum Field Theories With Compact Noncommutative Extra Dimensions
• Intersecting branes and a standard model realization in matrix models
• Noncommutative Quantum Mechanics and Seiberg-Witten Map
• Pair Production of Neutral Higgs Bosons through Noncommutative QED Interactions at Linear Colliders
• On the vacuum states for noncommutative gauge theory
• Instability of Non-Commutative SYM Theories at Finite Temperature
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Phenomenology of Particle Production and Propagation in String-Motivated Canonical Noncommutative Spacetime
• Space/time noncommutative field theories and causality
• Vacuum Birefringence as a Probe of Planck Scale Noncommutativity
• CP violation from noncommutative geometry
• Causal structures and holography
• Excitations in Hot Non-Commutative Theories
• Spacetime noncommutativity and ultra-high energy cosmic ray experiments
• Closed Strings Tachyons and Non-Commutative Instabilities
• Non-commutative SU(N) gauge theories and asymptotic freedom
• Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
• Superstatistics approach to path integral for a relativistic particle
• 8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• A Note on Noncommutative Chern-Simons Theories
• Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions
• Noncommutative epsilon-graded connections
• The absence of the 4$\psi$ divergence in noncommutative chiral models
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• The Noncommutative Supersymmetric Nonlinear Sigma Model
• Exact Results in Noncommutative $\mathcal{N}=2$ Supersymmetric Gauge Theories
• Quantum gauge theories on noncommutative 3-d space
• Constraining spacetime noncommutativity with primordial nucleosynthesis
• Constraining noncommutative field theories with holography
• Quantisation of θ-expanded non-commutative QED
• Noncommutative Solitons on Orbifolds
• Fermions and Emergent Noncommutative Gravity
• Infrared and ultraviolet cutoffs of quantum field theory
• UV/IR Mixing for Noncommutative Complex Scalar Field Theory, II (Interaction with Gauge Fields)
• Twisted Hopf symmetries of canonical noncommutative spacetimes and the no-pure-boost principle
• On the IR/UV mixing and experimental limits on the parameters of canonical noncommutative spacetimes
• Noncommutative geometry, gauge theory and renormalization
• Noncommutative Planar Particle Dynamics with Gauge Interactions
• The one-loop effective action for quantum electrodynamics on noncomutative space
• Noncommutative gauge theories and Lorentz symmetry
• The Three-Dimensional Noncommutative Nonlinear Sigma Model in Superspace
• Noncommutative gauge theory and symmetry breaking in matrix models
• Chiral Anomaly on Fuzzy 2-Sphere
• Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED${}_4$
• Non-Relativistic Non-Commutative Field Theory and UV/IR Mixing
• General structure of the photon self-energy in non-commutative QED
• Nonplanar Anomalies in Noncommutative Theories and the Green-Schwarz Mechanism
• Group velocity in noncommutative spacetime
• Gauge theories on quantum spaces
• Interplay between curvature and Planck-scale effects in astrophysics and cosmology
• Photon-neutrino interaction in theta-exact covariant noncommutative field theory
• Morita Duality and Large-N Limits
• Supertube domain-walls and elimination of closed time-like curves in string theory
• Trouble with space-like noncommutative field theory
• On the stringy nature of winding modes in noncommutative thermal field theories
• On non-commutative N=2 super Yang-Mills
• Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
• Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
• On the finiteness of noncommutative supersymmetric QED${}_3$ in the covariant superfield formulation
• D3-brane Holography
• Anomaly and Nonplanar Diagrams in Noncommutative Gauge Theories
• 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
• Casimir Effect on the Radius Stabilization of the Noncommutative Torus
• Deconstructing Noncommutativity with a Giant Fuzzy Moose
• Consistent noncommutative quantum gauge theories?
• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion
• Anomalous C-violating Three Photon Decay of the Neutral Pion in Noncommutative Quantum Electrodynamics
• Numerical Results for U(1) Gauge Theory on 2d and 4d Non-Commutative Spaces
• Noncommutative and Non-Anticommutative Quantum Field Theory
• Natural Cutoffs via Compact Symplectic Manifolds
• Telltale Traces of U(1) Fields in Noncommutative Standard Model Extensions
• Scalar field theories in a Lorentz-invariant three-dimensional noncommutative space-time
• Neutrino propagation in noncommutative spacetimes
• Entanglement Spheres and a UV-IR connection in Effective Field Theories
• On UV/IR mixing in noncommutative gauge field theories
• Perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory
• Toward simulating Superstring/M-theory on a quantum computer
• UV/IR mixing and the Goldstone theorem in noncommutative field theory
• Ultra-violet Finiteness in Noncommutative Supersymmetric Theories
• Introduction to Quantum-Gravity Phenomenology
• Open Wilson Lines and Generalized Star Product in Noncommutative Scalar Field Theories
• Self-energies on deformed spacetimes
• Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges
• On the UV renormalizability of noncommutative field theories
• Implications of Spacetime Quantization for the Bahcall-Waxman Neutrino Bound
• Matrix Bases for Star Products: a Review
• Holographic Brownian Motion in Magnetic Environments
• Scaling properties of the perturbative Wilson loop in two-dimensional non-commutative Yang-Mills theory
• Non--Commutative Field Theories beyond Perturbation Theory
• On Non-Commutative U*(1) Gauge Models and Renormalizability
• Noncommutativity, Extra Dimensions, and Power Law Running in the Infrared
• Exact Partition Functions for Gauge Theories on ${\mathbb{R}}_{\lambda }^3$
• Position-dependent noncommutative products: classical construction and field theory
• The Z--> l^+ l^- and W--> nu_l l^+ decays in the noncommutative standard model}}
• Dynamical Breaking of Supersymmetry in Noncommutative Gauge Theories
• Supergravity Dual of Noncommutative N=1 SYM
• Gauge Theories on Deformed Spaces
• Noncommutative gauge theories on ${\mathbb{R}}_{\lambda }^3$: Perturbatively finite models
• Matter-Antimatter Asymmetry Generated by Loop Quantum Gravity
• Higher-spin gravity and torsion on quantized space-time in matrix models
• The BRS invariance of noncommutative U(N) Yang-Mills theory at the one-loop level
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory
• On the Renormalizability of Noncommutative U(1) Gauge Theory - an Algebraic Approach
• Running couplings and triviality of field theories on non-commutative spaces
• Chiral effective potential in $\mathcal{N}=1/2$ non-commutative Wess-Zumino model
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Noncommutative Standard Modelling
• Particle phenomenology on noncommutative spacetime
• Non-Commutative Geometry from Strings
• The Noncommutative S-Matrix
• Lorentz Violation in the Higgs Sector and Noncommutative Standard Model
• A New Approach to Non-Commutative U(N) Gauge Fields
• A novel approach to non-commutative gauge theory
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• Non-commutative U(1) Super-Yang-Mills Theory: Perturbative Self-Energy Corrections
• The low energy limit of the non-commutative Wess-Zumino model
• Ultra-violet Finite Noncommutative Theories
• Free q-Deformed Relativistic Wave Equations by Representation Theory
• Seiberg-Witten maps and scattering amplitudes of NCQED
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• On the Operator Product Expansion in Noncommutative Quantum Field Theory
• Photon self-interaction on deformed spacetime
• Classical Solutions of the TEK Model and Noncommutative Instantons in Two Dimensions
• Renormalizability and Phenomenology of theta-expanded Noncommutative Gauge Field Theory
• Weak Gravity Conjecture for Noncommutative Field Theory
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Euler Top Dynamics of Nambu-Goto P-Branes
• Curvature and Gravity Actions for Matrix Models
• The Gribov problem in Noncommutative QED
• Effects of CPT and Lorentz Invariance Violation on Pulsar Kicks
• Constructions of Non Commutative Instantons on $T^4$ and $K_3$
• Divergences in Non-Commutative Gauge Theories with the Slavnov Term
• Gauge Independence of IR singularities in Non-Commutative QFT - and Interpolating Gauges
• Noncommutative U(1) gauge theory from a worldline perspective
• On the consistency of the three-dimensional noncommutative supersymmetric Yang-Mills theory
• BRST Quantization of Noncommutative Gauge Theories
• Seiberg-Witten map Invariant Scatterings
• Matrix Entanglement
• What lattice theorists can do for superstring/M-theory
• On the finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory
• Canonical Quantization of Noncommutative Field Theory
• Spontaneous reduction of noncommutative gauge symmetry and model building
• The inclusive b -> s γdecay in the noncommutative standard model
• On the energy-momentum tensor in Moyal space
• Noncommutativity and Model Building
• TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• A bound on the scale of spacetime noncommutativity from the reheating phase after inflation
• UV And IR Effects On Hawking Radiation
• On the Origin of the Harmonic Term in Noncommutative Quantum Field Theory
• On the continuity of the commutative limit of the 4d N=4 non-commutative super Yang-Mills theory
• Factorization and generalized *-products
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• One-loop Noncommutative U(1) Gauge Theory from Bosonic Worldline Approach
• Spin Flavor Conversion of Neutrinos in Loop Quantum Gravity
• O(3) Sigma model with Hopf term on Fuzzy Sphere
• Cancellation of soft and collinear divergences in noncommutative QED
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Aspects of Open-Closed Duality in a Background B-Field
• Do high-energy neutrinos travel faster than photons in a discrete space-time?
• Validity of Goldstone Theorem at Two Loops in Noncommutative U(N) Linear Sigma Model
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• A Noncommutative Version of the Minimal Supersymmetric Standard Model
• Noncommutativity from the string perspective: modification of gravity at a mm without mm sized extra dimensions
• Dynamics of O(N) Model in a Strong Magnetic Background Field as a Modified Noncommutative Field Theory
• Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
• Two-Point Functions on Deformed Spacetime
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• Aspects of Open-Closed Duality in a Background B-Field II
• Fundamental physics in space: a Quantum-Gravity perspective
• Hopf-algebra description of noncommutative-spacetime symmetries
• From UV/IR mixing to closed strings
• Anatomy of Two-Loop Effective Action in Noncommutative Field Theories
• Observations on non-commutative field theories in coordinate space
• Intersecting Noncommutative D-branes and Baryons in Magnetic Fields
• Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
• Aspects of noncommutative descriptions of planar systems in high magnetic fields
• On UV/IR Mixing via Seiberg-Witten Map for Noncommutative QED
• One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative 1/p**2 U(1) Gauge Model
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Interacting Dipoles from Matrix Formulation of Noncommutative Gauge Theories
• Non-commutative Geometry from Perturbative Quantum Gravity in de Sitter spacetime
• The Gribov problem in Noncommutative gauge theory
• Quantum instability of gauge theories on $\kappa$-Minkowski space
• (2+1)D Noncommutative CP${}^{N-1}$ Model
• Field Theory on a Non-commutative Plane: a Non-Perturbative Study
• First Simulation Results for the Photon in a Non-Commutative Space
• Quantum field theories on noncommutative R^4 versus theta-expanded quantum field theories
• Recursive Relations For Processes With n Photons Of Noncommutative QED
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Perturbative ultraviolet and infrared dynamics of noncommutative quantum field theory
• Noncommutative QED+QCD and $\beta$-function for QED
• Noncommutative Two-Dimensional Gauge Theories
• Neutrino-electron scattering in noncommutative space
• Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space
• Two-photon annihilation of singlet cold dark matters due to noncommutative space-time
• Higgs Couplings in NonCommutative Standard Model
• High-Temperature Effective Potential of Noncommutative Scalar Field Theory: Reduction of Degree of Freedom by Noncommutativity
• Aspects of perturbative quantum field theory on non-commutative spaces
• Non-commutative massive unquenched ABJM
• Photon polarization tensor on deformed spacetime: A four-photon-tadpole contribution
• On Evaluation of Nonplanar Diagrams in Noncommutative Field Theory
• All-loop finiteness of the two-dimensional noncommutative supersymmetric gauge theory
• A Vector Supersymmetry in Noncommutative U(1) Gauge Theory with the Slavnov Term
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Cornwall-Jackiw-Tomboulis effective potential for canonical noncommutative field theories
• UV-IR mixing and the quantum consistency of noncommutative gauge theories
• Renormalization of the energy-momentum tensor in noncommutative scalar field theory
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• Conformal Anomalies in Noncommutative Gauge Theories
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Strong Field, Noncommutative QED
• Soliton Solutions on Noncommutative Orbifold $ T^2/Z_4
• Fine-tuning problems in quantum field theory and Lorentz invariance: A scalar-fermion model with a physical momentum cutoff
• Noncommutative (supersymmetric) electrodynamics in the Yang-Feldman formalism
• Noncommutative supersymmetric Chern-Simons-matter model
• Anomalous anomalies from virtual black holes
• UV/IR Mixing in Noncommutative Field Theories and Open Closed String Duality
• The form factors existing in the b->s g^* decay and the possible CP violating effects in the noncommutative standard model
• Heisenberg Evolution in a Quantum Theory of Noncommutative Fields
• Dispersion relations for the self-energy in non-commutative field theories
• One-loop renormalization of general noncommutative Yang-Mills field model coupled to scalar and spinor fields
• Technical Remarks and Comments on the UV/IR-Mixing Problem of a Noncommutative Scalar Quantum Field Theory
• One Loop Renormalizability of Spontaneously Broken Gauge Theory with a Product of Gauge Groups on Noncommutative Spacetime: the U(1) x U(1) Case
• Quantization of a gauge theory on a curved noncommutative space
• Spectral theorem in noncommutative field theories: Jacobi dynamics
• Revisiting NCQED and scattering amplitudes
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• N=1/2 Supersymmetric gauge theory in noncommutative space
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Gravitational renormalization of quantum field theory: a "conservative" approach
• The role of the field redefinition in noncommutative Maxwell theory
• Matrix Models, Emergent Gravity, and Gauge Theory
• Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models
• Non-orientable string one-loop corrections in the presence of a B field
• Could the photon dispersion relation be non-linear ?
• Bounds on the scale of noncommutativity from mono photon production in ATLAS Runs -1 and -2 experiments at LHC energies
• Wave Propagation and IR/UV Mixing in Noncommutative Spacetimes
• Total momentum and other Noether charges for particles interacting in a quantum spacetime
• High-Energy Scattering in Non-Commutative Field Theory
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
• alpha^star-Cohomology and Classification of Translation-Invariant Non-Commutative Quantum Field Theories
• The role of the Seiberg-Witten field redefinition in renormalization of noncommutative chiral electrodynamics
• Supersymmetric Extension of the Snyder Algebra
• Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and Noncommutative Geometry
• Nonequilibrium Dynamics in Noncommutative Spacetime
• Separation of noncommutative differential calculus on quantum Minkowski space
• Supersymmetry and Gravity in Noncommutative Field Theories
• Seiberg-Witten map for the 4D noncommutative BF theory
• Noncommutative Supersymmetric Theories
• One-loop Photon's Effective Action in the Noncommutative Scalar QED${}_3$
• A Vector Supersymmetry Killing the Infrared Singularity of Gauge Theories in Noncommutative Space
• On the distance observable in the Moyal plane and in a novel two-dimensional space with string-theory pregeometry
• Fermions Coupled to Emergent Noncommutative Gravity
• Photon-neutrino interaction in theta-exact covariant noncommutative model: Phenomenology and Quantum properties*
• Perturbative Symmetries on Noncommutative Spaces
• Noncommutative spacetime geometry and one-loop effects in primordial cosmology
• A Note on UV/IR Mixing and Non-Commutative Instanton Calculus
• On the UV/IR mixing of Lie algebra-type noncommutatitive ${\varphi }^4$-theories
• A one-loop test for construction of 4D N=4 SYM from 2D SYM via fuzzy sphere geometry
• First numerical approach to a Grosse-Wulkenhaar model
• Some Aspects of Scattering in (Non) Commutative Gauge Theories
• Extended BRST formulation of a non-commutative U(1) gauge model
• The Photon Dispersion as an Indicator for New Physics ?
• D-branes, gauge/string duality and noncommutative theories
• Constraining the deformed dispersion relation with the hydrogen atom 1S-2S transition
• Aspects of noncommutativity in field theory, strings and membranes
• Noncommutative Jackiw-Pi model: One-loop renormalization
• Noncommutative $\mathcal{N}=2$ Chern-Simons-matter model
• Gauge theory models on $\kappa$-Minkowski space: Results and prospects
• UV/IR mixing in Noncommutative SU(N) Yang-Mills theory
• A Vector Supersymmetry Killing IR Divergences in Non-Commutative Gauge Theories