Spectral Networks
Spectral Networks
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DOI：
10.1007/s00023-013-0239-7
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
D. Gaiotto;G. Moore;Andrew Neitzke
中科院分区：
文献类型：
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作者：
D. Gaiotto;G. Moore;Andrew Neitzke
我们引入新的几何对象称为光谱网络。谱网络是黎曼曲面上的轨迹网络，它们遵循一定的局部规则。光谱网络自然地出现在与表面缺陷耦合的四维理论中，特别是S类理论。在这些理论中，谱网络为计算BPS简并度提供了一个有用的工具;网络直接确定了生活在表面缺陷上的孤子的简并度，这反过来又决定了生活在4d体中的粒子的简并度。谱网络也导致了一个新的映射之间的平面连接的二维surfaceC和平面阿贝尔连接的适当分支覆盖。这种构造在C上平坦连通的模空间上产生了自然坐标系，我们猜想它们是簇坐标系。
We introduce new geometric objects calledspectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensionaltheories coupled to surface defects, particularly the theories of classS. In these theories, spectral networks provide a useful tool for the computation of BPS degeneracies; the network directly determines the degeneracies of solitons living on the surface defect, which in turn determines the degeneracies for particles living in the 4d bulk. Spectral networks also lead to a new map between flatconnections on a two-dimensional surfaceCand flat abelian connections on an appropriate branched coverofC. This construction produces natural coordinate systems on moduli spaces of flatconnections onC, which we conjecture are cluster coordinate systems.