论文标题
$ \ MATHCAL {n} = 2 $ SUPESMYMETRIC $ {\ rm u}（1）^n $ gauge理论的1/2-bps涡流字符串
1/2-BPS vortex strings in $\mathcal{N}=2$ supersymmetric ${\rm U}(1)^N$ gauge theories
论文作者
论文摘要
$ \ Mathcal {n} = 2 $ supersymmetric $ {\ rm u}（1）^n $ garuge理论具有$ n $ hypermultiplets，以任意fayet-iliopoulos的通用设置为每个量规组的参数组和可逆的电荷矩阵的概括。尽管字符串张力通常是正方根形式的，但事实证明，所有现有的BPS（Bogomol'nyi-prasad-Sommerfield）溶液具有张力，在磁通量中是线性的，而磁通量又与绕组数字线性相关。主要结果是一系列定理，建立了所谓约束方程的三种不同类型的解决方案，可以将其描绘为$ {\ rm su}（2）_r $ space中磁通量的正交方向。在所有情况下，我们进一步证明了一个看似消失的Bogomol'nyi界限不能具有解决方案。最后，我们以类似于主形式和类似陶比的形式写下最通用的涡旋方程。值得注意的是，最终的漩涡方程本质上是Abelian，因为在求解约束方程后，方程中没有$ {\ rm su}（2）_r $对称的痕迹。
Strings in $\mathcal{N}=2$ supersymmetric ${\rm U}(1)^N$ gauge theories with $N$ hypermultiplets are studied in the generic setting of an arbitrary Fayet-Iliopoulos triplet of parameters for each gauge group and an invertible charge matrix. Although the string tension is generically of a square-root form, it turns out that all existing BPS (Bogomol'nyi-Prasad-Sommerfield) solutions have a tension which is linear in the magnetic fluxes, which in turn are linearly related to the winding numbers. The main result is a series of theorems establishing three different kinds of solutions of the so-called constraint equations, which can be pictured as orthogonal directions to the magnetic flux in ${\rm SU}(2)_R$ space. We further prove for all cases, that a seemingly vanishing Bogomol'nyi bound cannot have solutions. Finally, we write down the most general vortex equations in both master form and Taubes-like form. Remarkably, the final vortex equations essentially look Abelian in the sense that there is no trace of the ${\rm SU}(2)_R$ symmetry in the equations, after the constraint equations have been solved.
