Nonabelian gauge field and dual description of fuzzy sphere
Nonabelian gauge field and dual description of fuzzy sphere
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DOI：
10.1088/1126-6708/2004/04/058
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发表时间：
2004-02
影响因子：
5.4
通讯作者：
Y. Kimura
中科院分区：
文献类型：
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作者：
Y. Kimura
在矩阵模型中，高维D-膜是通过对低维D-膜的坐标施加非对易关系来获得的。另一方面，这种非对易空间的对偶描述是由具有规范场的高维D-膜提供的。在恒定的R-R场强背景中，模糊球体可以表现为低维D-膜的构型。本文通过在高维球面D-膜上引入非阿贝尔规范场，考虑了高维模糊球面的对偶刻画。利用Born-Infeld作用量，我们证明了当n较大时，具有非阿贝尔规范场的模糊2k-球和具有非平凡Chern特征的球D2k-膜是相同的物体。讨论了非对易几何与非阿贝尔规范场之间的关系。非阿贝尔规范场由包含坐标依赖的非对易矩阵表示。我们还研究了它与量子霍尔系统的相似性。
In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher dimensional D-branes with gauge fields. Fuzzy spheres can appear as a configuration of lower dimensional D-branes in a constant R-R field strength background. In this paper, we consider a dual description of higher dimensional fuzzy spheres by introducing nonabelian gauge fields on higher dimensional spherical D-branes. By using the Born-Infeld action, we show that a fuzzy 2k-sphere and spherical D2k-branes with a nonabelian gauge field whose Chern character is nontrivial are the same objects when n is large. We discuss a relationship between the noncommutative geometry and nonabelian gauge fields. Nonabelian gauge fields are represented by noncommutative matrices including the coordinate dependence. A similarity to the quantum Hall system is also studied.