Noncommutative Gauge Theories from Deformation Quantization

Abstract

We construct noncommutative gauge theories based on the notion of the Weyl bundle, which appears in Fedosov's construction of deformation quantization on an arbitrary symplectic manifold. These correspond to D-brane worldvolume theories in non-constant B-field and curved backgrounds in string theory. All such theories are embedded into a "universal" gauge theory of the Weyl bundle. This shows that the combination of a background field and a noncommutative field strength has universal meaning as a field strength of the Weyl bundle. We also show that the gauge equivalence relation is a part of such a "universal" gauge symmetry.

23 pages, LaTeX2e, Final version published in Nucl.Phys.B

References in corpus (4)

• String Theory and Noncommutative Geometry
• D-branes and Deformation Quantization
• Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres
• Comments on Gauge Equivalence in Noncommutative Geometry

Cited by in corpus (10)

• Noncommutative Field Theory
• Second order expansions of action functionals of noncommutative gauge theories
• Wick type deformation quantization of Fedosov manifolds
• D-branes on Group Manifolds and Deformation Quantization
• Symplectic connections, Noncommutative Yang Mills theory and Supermembranes
• Hamiltonian formulation of Noncommutative D3--Brane
• Tensor calculus on noncommutative spaces
• The U(1)A anomaly in noncommutative SU(N) theories
• The Fuzzy Kaehler Coset Space with the Darboux Coordinates
• Effective Action for D-branes on SU(2)/U(1) Gauged WZW Model