There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-Abelian. We show that we can use tachyon condensation to determine the position or the shape of D0-branes uniquely as a commutative region in spacetime together with a non-trivial gauge flux on it, even if the scalar fields are non-Abelian. We use the idea of the so-called coherent state method developed in the field of matrix models in the context of the tachyon condensation. We investigate configurations of non-commutative D2-brane made out of D0- branes as examples. In particular, we examine a Moyal plane and a fuzzy sphere in detail, and show that whose shapes are commutative ℝ2 and S2, respectively, equipped with uniform magnetic flux on them.We study the physical meaning of this commutative geometry made out of matrices, and propose an interpretation in terms of K-homology.
ASJC Scopus subject areas
- Physics and Astronomy(all)