Spherical D-brane by tachyon condensation

Abstract

We find a novel tachyon condensation which provides a D-brane system with spherical worldvolume in the flat spacetime. The tachyon profile is a deformation of a known D0-brane solution on non-BPS D3-branes in type IIA superstring theory, which realizes a bound state of a spherical D2-brane and a D0-brane. The D0-brane is resolved into the sphere as a U (1) monopole flux of the unit magnetic charge. We show that the system has the correct tension and the RRcoupling. Although the low energy effective action of the system is the same as that of the dual description of the fuzzy sphere solution of multiple D0-branes, our system cannot be equivalent to the fuzzy sphere. We argue that the sphere can be stable in a certain RR-flux background.The use of projective modules in describing the tachyon condensation is emphasized.

Matrix model and Yukawa couplings on the noncommutative torus

“…Recently, in Refs. [22,23], the authors showed that the magnetic flux may come from the tachyon condensations induced from the dynamics of D-branes and non-BPS D-branes. We expect that our results can be described by the full dynamics of the IKKT model.…”

Commutative geometry for non-commutative D-branes by tachyon condensation

“…In the case that the tachyon potential has the form (2.8), this gauge field is also confined to the region M ⊂ R 3 because of the delta-function distribution. In this case, (2.12) has components only along M (for the proof, see [22]). If U(x) is not globally defined and there are two different diagonalizations {U I (x)} at a point, then two gauge potentials of the form (2.12) are related by U(1) transition function.…”

“…The resulting defect should be the deformation of the point-like defect by matrices Φ. Indeed, as shown in [22], a deformation of the single D0-brane (k = 1) profile drastically changes the condensation defect to a spherical D2-brane 1 . Our claim in this paper is that the position or the shape of D-branes is determined by diagonalizing the tachyon field T , not the scalar fields Φ themselves.…”

“…a) The term σ · x in (3.24) is independent of the choice of Φ, and it can be diagonalized only patch-wise [22].…”

“…Technically our analysis in this paper is an application of the technique developed so far [19]. This method has been applied to realize the Nahm construction of monopoles and the ADHM construction of instantons [20,21] and/or to realize a spherical D-brane [22]. In the latter case, a system of 2 non-BPS D3-branes is considered, where a tachyon profile T representing a D0-brane is deformed by a constant shift.…”