The extended Bogomolny equations and generalized Nahm pole boundary condition
The extended Bogomolny equations and generalized Nahm pole boundary condition
复制标题
扩展的Bogomolny方程和广义Nahm极边界条件
作者：
Siqi He;R. Mazzeo
本文建立了推广的Bogomolny方程的解与稳定的$SL(2，mathbb{R})$Higgs丛的Hitchin分支之间的Kobayashi-Hitchin型对应，从而验证了Gaiotto和Witten的猜想.我们还建立了与稳定的$SL(2，mathbb{R})$Higgs丛的模空间中的非Hitchin分支相对应的部分Kobayashi-Hitchin对应。我们还证明了$mathbb{C}irp$上具有结点奇点的解的存在唯一性。
In this paper we develop a Kobayashi-Hitchin type correspondence between solutions of the extended Bogomolny equations on $Sigma imes RP$ with Nahm pole singularity at $Sigma imes {0}$ and the Hitchin component of the stable $SL(2,mathbb{R})$ Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop a partial Kobayashi-Hitchin correspondence for solutions with a knot singularity in this program, corresponding to the non-Hitchin components in the moduli space of stable $SL(2,mathbb{R})$ Higgs bundles. We also prove existence and uniqueness of solutions with knot singularities on $mathbb{C} iRP$.