Noncommutativity and Tachyon Condensation

Abstract

We study the fuzzy or noncommutative Dp-branes in terms of infinitely many unstable D0-branes, from which we can construct any Dp-branes. We show that the tachyon condensation of the unstable D0-branes induces the noncommutativity. In the infinite tachyon condensation limit, most of the unstable D0-branes disappear and remaining D0-branes are actually the BPS D0-branes with the correct noncommutative coordinates. For the fuzzy S^2 case, we explicitly show only the D0-branes corresponding to the lowest Landau level survive in the limit. We also show that a boundary state for a Dp-brane satisfying the Dirichlet boundary condition on a curved submanifold embedded in the flat space is not localized on the submanifold. This implies that the Dp-brane on it is ambiguous at the string scale and solves the problem for a spherical D2-brane with a unit flux on the world volume which should be equivalent to one D0-brane. We also discuss the diffeomorphism in the D0-brane picture.

30 pages, references added, minor corrections and clarifications, version to appear in JHEP

References in corpus (3)

• c=1 Matrix Model from String Field Theory
• Relating branes and matrices
• Boundary String Field Theory as a Field Theory -- Mass Spectrum and Interaction

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• The matrix regularization for Riemann surfaces with magnetic fluxes
• Laplacians on Fuzzy Riemann Surfaces
• Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
• Supertubes in Matrix model and DBI action
• Diffeomorphisms on Fuzzy Sphere
• Spherical D-brane by Tachyon Condensation