Noncommutativity and Tachyon Condensation

TL;DR

This paper explores how tachyon condensation in unstable D0-branes leads to noncommutative Dp-branes, demonstrating the emergence of noncommutativity and analyzing boundary states and diffeomorphisms in this framework.

Contribution

It shows that tachyon condensation induces noncommutativity in D-branes and clarifies the nature of Dp-branes as limits of unstable D0-branes, including explicit examples like fuzzy spheres.

Findings

Tachyon condensation causes unstable D0-branes to form noncommutative Dp-branes.

In the condensation limit, only lowest Landau level D0-branes survive for fuzzy S^2.

Boundary states for Dp-branes are not localized on the submanifold, indicating ambiguity at the string scale.

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.