Nahm transform and moduli spaces of CP**N models on the torus
Nahm transform and moduli spaces of CP**N models on the torus
复制标题
圆环上 CP**N 模型的 Nahm 变换和模空间
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
A. Wipf
中科院分区：
文献类型：
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作者：
Miguel Aguado;M. Asorey;A. Wipf
二维规范场的Nahm变换建立了定义在环面上的带拓扑荷k的U（N）规范场的轨道空间与定义在对偶环面上的带拓扑荷N的U（k）规范场的轨道空间之间的一一对应。本文的主要结果是证明了C PN瞬子不存在类似的对偶变换。这一事实建立了四维规范理论和C PN模型之间的显著差异。结果如下从一个完整的和明确的参数化的所有自对偶解决方案的基础上的2维环面的瞬子的模空间的全球分析。正则瞬子空间的边界与奇异瞬子空间一致。这一识别提供了一种新的方法来分析重叠瞬子在C-PN-sigma模型的红外扇区中的作用。
Abstract There is a Nahm transform for 2-dimensional gauge fields which establishes a one-to-one correspondence between the orbit space of U(N) gauge fields with topological charge k defined on a torus and that of U(k) gauge fields with charge N on the dual torus. The main result of this paper is to show that a similar duality transform cannot exist for C PN instantons. This fact establishes a significative difference between 4-D gauge theories and C PN models. The result follows from the global analysis of the moduli space of instantons based on a complete and explicit parametrization of all self-dual solutions on the 2-dimensional torus. The boundary of the space of regular instantons is shown to coincide with the space of singular instantons. This identification provides a new approach to analyzing the role of overlapping instantons in the infrared sector of C PN sigma models.