Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
Commutative Geometry for Non-commutative D-branes by Tachyon Condensation
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基于快子凝聚的非交换 D 膜的交换几何
DOI：
10.1093/ptep/pty062
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发表时间：
2018
影响因子：
3.5
通讯作者：
S. Matsuura and H. Muraki
中科院分区：
文献类型：
--
作者：
T. Asakawa;G. Ishiki;T. Matsumoto;S. Matsuura and H. Muraki
当 D 膜上的标量场是非阿贝尔场时，定义 D 膜的位置会很困难。我们证明，即使标量场是非阿贝尔场，我们也可以使用快子凝聚来确定 D0 膜的位置或形状，作为时空中的交换域，以及其上的非平凡规范通量。我们在快子凝聚的背景下使用了在矩阵模型领域开发的所谓相干态方法的思想。我们以 D0 膜为例研究非交换 D2 膜的构型。特别是，我们详细研究了莫亚尔平面和模糊球体，并表明它们的形状是可交换的，并且分别在它们上配备有均匀磁通量。我们研究了这种由矩阵组成的交换几何的物理意义，并提出了 K-同调的解释。
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 commutativeand, 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.