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

Asakawa, Tsuguhiko (Department of Integrated Design Engineering, Maebashi Institute of Technology, Maebashi 371-0816, Japan) ; Ishiki, Goro (Tomonaga Center for the History of the Universe, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan) (Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan) ; Matsumoto, Takaki (Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan) ; Matsuura, So (Department of Physics, Hiyoshi Campus, and Research and Education Center for Natural Science, Keio University, 4-1-1 Hiyoshi, Yokohama 223-8521, Japan) ; Muraki, Hisayoshi (Department of Physics, Sogang University, Seoul 04107, Korea)

30 January 2019

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 and , 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.


Published in: PTEP 2018 (2018) 063B04
Published by: Oxford University Press/Physical Society of Japan
DOI: 10.1093/ptep/pty062
arXiv: 1804.00161
License: CC-BY-3.0



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