D-branes, Symplectomorphisms and Noncommutative Gauge Theories

Abstract

It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A noncommutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theories may be described in terms of symplectic connections on symplectic fibrations. The world volume being its base manifold and the (sub)group of volume preserving diffeomorphisms generate the symplectomorphisms which preserve the (infinite dimensional) Poisson bracket of the fibration.

Changed content. Invited talk to SSQFT2000, Kharkov; Latex, espcrc2.sty, 7 pages

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Cited by in corpus (17)

• On the spectrum of a matrix model for the D=11 supermembrane compactified on a torus with non-trivial winding
• Spectral properties in supersymmetric matrix models
• SL(2,Z) symmetries, Supermembranes and Symplectic Torus Bundles
• The Supermembrane with Central Charges on a G2 Manifold
• The supermembrane with central charges:(2+1)-D NCSYM, confinement and phase transition
• Geodesic analysis and black hole shadows on a general non--extremal rotating black hole in five--dimensional gauged supergravity
• Supermembrane origin of type II gauged supergravities in 9D
• Nonperturbative SL(2,Z) (p,q)-strings manifestly realized on the quantum M2
• Classification of M2-brane 2-torus bundles, U-duality invariance and type II gauged supergravities
• The Minimally Immersed 4D Supermembrane
• Spinning solutions for the bosonic M2-brane with $C_{\pm }$ fluxes
• On the Geometry of Sculpting-like Gauging Processes
• A New Mechanism for Gauging a Theory
• On the Spectral properties of Multi-branes, M2 and M5 branes
• On global aspects of duality invariant theories: M2-brane vs DFT
• D2-brane with RR and NSNS fluxes and its dual M-theory origin
• Update on the quantum properties of the Supermembrane