General Properties of Noncommutative Field Theories

Abstract

In this paper we study general properties of noncommutative field theories obtained from the Seiberg-Witten limit of string theories in the presence of an external B-field. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with space-space noncommutativity. We analyze as well questions associated to the spin-statistics connections, and show that noncommutative N=4, U(1) gauge theory can be softly broken to N=0 satisfying the axioms and providing an example where the Wilsonian low energy effective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative.

39 pages. LaTeX. 4 figures. Typos corrected. Comments and references added. To appear in Nuclear Physics B

References in corpus (4)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• The quantum structure of spacetime at the Planck scale and quantum fields
• The photon-neutrino interaction in non-commutative gauge field theory and astrophysical bounds
• Closed Strings Tachyons and Non-Commutative Instabilities

Cited by in corpus (118)

• Quantum Spacetime Phenomenology
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
• New concept of relativistic invariance in NC space-time: twisted Poincaré symmetry and its implications
• Spin and Statistics on the Groenewold-Moyal Plane: Pauli-Forbidden Levels and Transitions
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Supersymmetry in noncommutative superspaces
• Wedge-Local Quantum Fields and Noncommutative Minkowski Space
• CPT Violation Does Not Lead to Violation of Lorentz Invariance and Vice Versa
• Field Theory on Noncommutative Spacetimes: Quasiplanar Wick Products
• M-Theory on Deformed Superspace
• Twist and Spin-Statistics Relation in Noncommutative Quantum Field Theory
• Vacuum Birefringence as a Probe of Planck Scale Noncommutativity
• Spacetime noncommutativity and ultra-high energy cosmic ray experiments
• Causal structures and holography
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
• Cosmic Rays and the Search for a Lorentz Invariance Violation
• Adding flavor to the gravity dual of non-commutative gauge theories
• Constraining noncommutative field theories with holography
• Lorentz Invariance And Unitarity Problem In Non-Commutative Field Theory
• Noncommutative spacetime symmetries: Twist versus covariance
• Noncommutative gauge theories and Lorentz symmetry
• Newton equation for canonical, Lie-algebraic and quadratic deformation of classical space
• Unitarity of Time-Like Noncommutative Gauge Theories: The Violation of Ward Identities in Time-Ordered Perturbation Theory
• Deformation of the ABJM Theory
• Trouble with space-like noncommutative field theory
• Noncommutative Synchrotron
• Noncommutativity and theta-locality
• Star product algebras of test functions
• Telltale Traces of U(1) Fields in Noncommutative Standard Model Extensions
• On UV/IR mixing in noncommutative gauge field theories
• Noncommutative Quantum Field Theory: A Confrontation of Symmetries
• Axiomatic formulations of nonlocal and noncommutative field theories
• Noncommutative fermions and quarkonia decays
• On general properties of Lorentz invariant formulation of noncommutative quantum field theory
• Comment on "Noncommutative gauge theories and Lorentz symmetry, Phys. Rev. D {\bf 70}, 125004 (2004) by R.Banerjee, B.Chakraborty and K.Kumar"
• Testing Noncommutative Spacetimes and Violations of the Pauli Exclusion Principle with underground experiments
• The BV Formalization of Chern-Simons Theory on Deformed Superspace
• Black Hole Geometries in Noncommutative String Theory
• Noncommutativity, Extra Dimensions, and Power Law Running in the Infrared
• Moyal multiplier algebras of the test function spaces of type S
• No UV/IR Mixing in Unitary Space-Time Noncommutative Field Theory
• Chiral effective potential in $\mathcal{N}=1/2$ non-commutative Wess-Zumino model
• Particle phenomenology on noncommutative spacetime
• Noncommutative Standard Modelling
• Quantum duality under the theta-exact Seiberg-Witten map
• Lorentz-invariant CPT violation
• Locality, Causality and Noncommutative Geometry
• An anthology of non-local QFT and QFT on noncommutative spacetime
• Equivalence of quantum field theories related by the theta-exact Seiberg-Witten map
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Quantum Fields on the Groenewold-Moyal Plane: C, P, T and CPT
• Generalized uncertainty principle in graphene
• A New Derivation of the CPT and Spin-Statistics Theorems in Non-Commutative Field Theories
• Quantized equations of motion in non-commutative theories
• On the Vacuum Cherenkov Radiation in Noncommutative Electrodynamics and the Elusive Effects of Lorentz Violation
• TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams
• Twisted convolution and Moyal star product of generalized functions
• Discrete Symmetries In Lorentz-Invariant Non-Commutative QED
• Ultrahyperfunctional Approach to Non-Commutative Quantum Field Theory
• Two-Point Functions on Deformed Spacetime
• Effective actions, Wilson lines and the IR/UV mixing in noncommutative supersymmetric gauge theories
• Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED
• 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
• Asymptotic approach to Special Relativity compatible with a relativistic principle
• Space-time: Commutative or noncommutative ?
• The U(1)A anomaly in noncommutative SU(N) theories
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• Dispersion relations in the noncommutative ϕ^3 and Wess-Zumino model in the Yang-Feldman formalism
• Analyticity of the Scattering Amplitude, Causality and High-Energy Bounds in Quantum Field Theory on Noncommutative Space-Time
• Noncommutative deformations of quantum field theories, locality, and causality
• Emergent Noncommutative gravity from a consistent deformation of gauge theory
• Twisted invariances of noncommutative gauge theories
• Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
• Wedge locality and asymptotic commutativity
• Canonical, Lie-algebraic and quadratic twist deformations of Galilei group
• Magnetic Monopole in Noncommutative Space-Time and Wu-Yang Singularity-Free Gauge Transformations
• Super Yang-Mills and theta-exact Seiberg-Witten map: Absence of quadratic noncommutative IR divergences
• Failure of microcausality in noncommutative field theories
• Carrier cones of analytic functionals
• Light-Like Noncommutativity, Light-Front Quantization and New Light on UV/IR Mixing
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
• CP violation, massive neutrinos, and its chiral condensate: new results from Snyder noncommutative geometry
• Planar and Nonplanar Konishi Anomalies and Effective Superpotential for Noncommutative N=1 Supersymmetric U(1)
• Emergence of Time from Dimensional Reduction in Noncommutative Geometry
• Laboratory frame analysis of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering in the Noncommutative Standard Model
• Noncommutative Time in Quantum Field Theory
• Past and future blurring at fundamental length scale
• Quantum black holes as classical space factories
• Non-Commutative (Softly Broken) Supersymmetric Yang-Mills-Chern-Simons
• Källén-Lehmann representation of noncommutative quantum electrodynamics
• Dealing with T and CPT violations in mixing as well as direct and indirect CP violations for neutral mesons decaying to two vectors
• Holographic flavor in the gauge/gravity duality
• On the Borchers Class of a Non-Commutative Field
• Causality in Non-Commutative Quantum Field Theories
• Reconstruction of universal Drinfeld twists from representations
• Nonequilibrium Dynamics in Noncommutative Spacetime
• Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
• Reciprocal of the CPT theorem
• Photon Defects in Noncommutative Standard Model Candidates
• Effective Field Theory of a Locally Noncommutative Space-Time and Extra Dimensions
• The Lorentz Group, Noncommutative Space-Time, and Nonlinear Electrodynamics in Majorana-Oppenheimer Formalism
• On Finite Noncommutativity in Quantum Field Theory
• Perturbative Symmetries on Noncommutative Spaces
• A Note on UV/IR Mixing and Non-Commutative Instanton Calculus
• Haag's Theorem in Noncommutative Quantum Field Theory
• Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory. II
• A note on the implementation of Poincaré symmetry in noncommutative field theory
• Photon-neutrino interaction in theta-exact covariant noncommutative model: Phenomenology and Quantum properties*
• Irreducibility of the set of field operators in Noncommutative Quantum Field Theory
• Renormalization Group Flow for Noncommutative Fermi Liquids
• N=1/2 Global SUSY: R-Matrix Approach
• Wick rotation for quantum field theories on degenerate Moyal space(-time)
• Aspects of noncommutativity in field theory, strings and membranes
• Energy renormalization and integrability within the massive neutrinos model
• D-branes, actions effectives et symétrie miroir