### Abstract

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 ℝ^{2} and S_{2}, 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.

Original language | English |
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Article number | 063B04 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2018 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2018 Jun 1 |

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### Keywords

- B23
- B26
- B82
- B83

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2018*(6), [063B04]. https://doi.org/10.1093/ptep/pty062