Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory
Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory
复制标题
周期单极子的 Nahm 变换¶和 ?=2 超杨-米尔斯理论
DOI：
10.1007/pl00005558
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发表时间：
2000
影响因子：
2.4
通讯作者：
A. Kapustin
中科院分区：
文献类型：
--
作者：
Sergey A. Cherkis;A. Kapustin
翻译后摘要：我们研究Bogomolny方程的102 ×？1.虽然他们不承认非平凡的有限能量的解决方案，我们表明，有有趣的无限能量的解决方案与希格斯场的增长在无穷远。我们称这些解为周期性单极子。利用Nahm变换，我们证明了周期性单极子与希钦方程的解一一对应，希格斯场在无穷远处呈指数增长。周期性单极子的模空间属于一类新的超凯勒流形，并在量子规范理论和弦理论中有应用。例如，我们证明了k个周期性单极子的模空间提供了？2.规范群SU（k）紧化在任意半径圆上的超杨-米尔斯理论。
Abstract: We study Bogomolny equations on ℝ2×?1. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperkähler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius.