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arXiv · hep-th/0402044

Nonabelian gauge field and dual description of fuzzy sphere

Yusuke Kimura
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Abstract

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 D$2k$-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.

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Yusuke Kimura. 2005-10-18. Nonabelian gauge field and dual description of fuzzy sphere. https://doi.org/10.1088/1126-6708%2F2004%2F04%2F058

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