Construction of Gauge Theories on Curved Noncommutative Spacetime

Abstract

We present a method where derivations of star-product algebras are used to build covariant derivatives for noncommutative gauge theory. We write down a noncommutative action by linking these derivations to a frame field induced by a nonconstant metric. An example is given where the action reduces in the classical limit to scalar electrodynamics on a curved background. We further use the Seiberg-Witten map to extend the formalism to arbitrary gauge groups. A proof of the existence of the Seiberg-Witten-map for an abelian gauge potential is given for the formality star-product. We also give explicit formulas for the Weyl ordered star-product and its Seiberg-Witten-maps up to second order.

35 pages, v2: references added, v3: PACS added, v4: final version, changes in the order of presentation

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Cited by in corpus (35)

• A Gravity Theory on Noncommutative Spaces
• Symmetry, Gravity and Noncommutativity
• The Standard Model on Non-Commutative Space-Time: Electroweak Currents and Higgs Sector
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Lie algebraic Noncommutative Gravity
• Star products made (somewhat) easier
• Noncommutative $R^d$ via closed star product
• The deformation quantizations of the hyperbolic plane
• Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• A symmetry invariant integral on kappa-deformed spacetime
• Semiclassical Lindblad master equation for spin dynamics
• Towards A Background Independent Quantum Gravity
• Position-dependent noncommutative products: classical construction and field theory
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Non-commutative gauge theory on D-branes in Melvin Universes
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Nonassociative Weyl star products
• Quantization of Emergent Gravity
• Feynman problem in the noncommutative case
• On Supergravity Solutions of Branes in Melvin Universes
• Gauge field theories with covariant star-product
• Bootstrapping Non-commutative Gauge Theories from L${}_{\infty }$ algebras
• On Coordinate Transformations in Planar Noncommutative Theories
• Non-constant Non-commutativity in 2d Field Theories and a New Look at Fuzzy Monopoles
• On beta-deformations and Noncommutativity
• Noncommutative theories and general coordinate transformations
• Dixmier traces on noncompact isospectral deformations
• A Perturbative Approach to Fuzzifying Field Theories
• NC Wilson lines and the inverse Seiberg-Witten map for nondegenerate star products
• Field Theory with Coordinate Dependent Noncommutativity
• Deformations of anti-de Sitter black holes
• Symplectic Fluctuations for Electromagnetic Excitations of Hall Droplets
• Electromagnetic Excitations of Hall Systems on Four Dimensional Space
• Theories on noncommutative spaces and deformed symmetries