Effective Field Theories on Non-Commutative Space-Time

Abstract

We consider Yang-Mills theories formulated on a non-commutative space-time described by a space-time dependent anti-symmetric field ${\theta }^{\mu \nu }(x)$. Using Seiberg-Witten map techniques we derive the leading order operators for the effective field theories that take into account the effects of such a background field. These effective theories are valid for a weakly non-commutative space-time. It is remarkable to note that already simple models for ${\theta }^{\mu \nu }(x)$ can help to loosen the bounds on space-time non-commutativity coming from low energy physics. Non-commutative geometry formulated in our framework is a potential candidate for new physics beyond the standard model.

arXiv comment22 pages, 1 figure

References in corpus (34)

• String Theory and Noncommutative Geometry
• Deformation quantization of Poisson manifolds, I
• Noncommutative Field Theory
• Quantum gravity and minimum length
• Noncommutative Field Theory and Lorentz Violation
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• D-branes and Deformation Quantization
• Gauge Theory on Noncommutative Spaces
• A path integral approach to the Kontsevich quantization formula
• Perturbative analysis on infrared aspects of noncommutative QED on R^4
• The Standard Model on Non-Commutative Space-Time
• Construction of non-Abelian gauge theories on noncommutative spaces
• Enveloping algebra valued gauge transformations for non-abelian gauge groups on non-commutative spaces
• Nonassociative Star Product Deformations for D-brane Worldvolumes in Curved Backgrounds
• Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale
• Signals for Non-Commutative Interactions at Linear Colliders
• Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R^4
• Review of the Phenomenology of Noncommutative Geometry
• Bounding Noncommutative QCD
• Comments on Non-Commutative Phenomenology
• Noncommutative gauge theory for Poisson manifolds
• Holography and String Dynamics in Time-dependent Backgrounds
• Noncommutative Gauge Theory without Lorentz Violation
• Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map
• The Gauge Anomaly and the Seiberg-Witten Map
• Noncommutativity in a Time-Dependent Background
• Lorentz-Invariant Non-Commutative Space-Time Based On DFR Algebra
• CP violation from noncommutative geometry
• Deformed QED via Seiberg-Witten Map
• Lorentz-Invariant Non-Commutative QED
• The Seiberg-Witten Map for a Time-dependent Background
• Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I
• Possible Effects of Noncommutative Geometry on Weak CP Violation and Unitarity Triangles
• Introduction to a Non-Commutative Version of the Standard Model

Cited by in corpus (32)

• Symmetry, Gravity and Noncommutativity
• Gauge Theories under Incorporation of a Generalized Uncertainty Principle
• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• Testing the Noncommutative Standard Model at a Future Photon Collider
• What are the Bounds on Space-Time Noncommutativity?
• Construction of Gauge Theories on Curved Noncommutative Spacetime
• Space-Time Symmetries of Noncommutative Spaces
• The UV/IR Interplay in Theories with Space-time Varying Non-commutativity
• Electroweak Theory with a Minimal Length
• Phenomenology of Lorentz-Conserving Noncommutative QED
• Minimal Scales from an Extended Hilbert Space
• Position-dependent noncommutative products: classical construction and field theory
• Möller and Bhabha scattering in the noncommutative standard model
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Non-commutative gauge theory on D-branes in Melvin Universes
• Drell-Yan as an avenue to test noncommutative Standard Model at the Large Hadron Collider
• Quantum Electrodynamics on Noncommutative Spacetime
• SL(2,C) gravity on noncommutative space with Poisson structure
• On Supergravity Solutions of Branes in Melvin Universes
• Canonical Noncommutativity Algebra for the Tetrad Field in General Relativity
• On Coordinate Transformations in Planar Noncommutative Theories
• Inferring the covariant $\Theta$-exact noncommutative coupling in the top quark pair production at linear colliders
• U(2,2) gravity on noncommutative space with symplectic structure
• Noncommutative theories and general coordinate transformations
• Search for associated production of Higgs with Z boson in the noncommutative Standard Model at linear colliders
• Effect of earth rotation on pair production of Standard Model Higgs bosons at linear colliders in the noncommutative space-time
• Laboratory frame analysis of $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ scattering in the Noncommutative Standard Model
• Symmetries, Microcausality and Physics on Canonical Noncommutative Spacetime
• Field Theory with Coordinate Dependent Noncommutativity
• Grand Unification on Noncommutative Spacetime
• Gravitational Anomalies in Noncommutative Field Theory
• ${\pi }^{+}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ colliding in noncommutative space