论文标题
来自ADHM双曲线单极管的光谱曲线
Spectral curves of hyperbolic monopoles from ADHM
论文作者
论文摘要
双曲线空间中的磁单孔与迷你扭转空间中的某些代数曲线（称为光谱曲线）对应，这些曲线又与Riemann Spheres之间的有理图相对应。双曲线单孔对应于圆形阳米尔斯instantons，并鉴定了单极和激数数，提供双曲空间的曲率被调整为由希格斯场的渐近幅度指定的值。在先前的工作中，已经确定了对ADHM Instanton数据的限制，该数据提供了对圆对称性的非典型实现，从而保留了双曲线空间球模型中旋转的标准作用。此处是针对光谱曲线的公式和双曲线单极的合理图，该公式就其受约束的ADHM矩阵而言。这扩展了较早的结果，仅适用于JNR类型的Instantons的子类。该公式用于获得超出JNR类的光谱曲线的新示例。
Magnetic monopoles in hyperbolic space are in correspondence with certain algebraic curves in mini-twistor space, known as spectral curves, which are in turn in correspondence with rational maps between Riemann spheres. Hyperbolic monopoles correspond to circle-invariant Yang-Mills instantons, with an identification of the monopole and instanton numbers, providing the curvature of hyperbolic space is tuned to a value specified by the asymptotic magnitude of the Higgs field. In previous work, constraints on ADHM instanton data have been identified that provide a non-canonical realization of the circle symmetry that preserves the standard action of rotations in the ball model of hyperbolic space. Here formulae are presented for the spectral curve and the rational map of a hyperbolic monopole in terms of its constrained ADHM matrix. This extends earlier results that apply only to the subclass of instantons of JNR type. The formulae are applied to obtain new explicit examples of spectral curves that are beyond the JNR class.
