论文标题
等级2分类问题III：具有其他自动形态的曲线
The rank-2 classification problem III: curves with additional automorphisms
论文作者
论文摘要
这是一系列论文中的第三份，概述了$ \ Mathcal {n} {=} 2 $ SuperCongry Field Field Theories通过其库仑分支几何形状的研究。在这里，我们将库仑分支几何形状的编码作为塞伯格（Seiberg）的曲线和1型的编码具有较大的重新对准不变性。虽然总是有一种固定这种不变性的独特方法，使得曲线和1形式是在库仑分支上单个价值的 - 本系列前两篇论文中使用的曲线的“规范框架”，还有其他有用的曲线是单值，但允许1Form允许使用1Form。在这些框架中，我们称之为“自动形态框架”，该框架是定期进行的，直到自动形态扭曲。我们认为，自动形态框架的多价值可以简化找到新一致的规模不变解决方案的计算复杂性。我们在一个示例中通过使用自动形态框架首次构建了$ \ Mathcal {n} {=} {=} 4 $ SU（3）Superyang-Mills理论，这是一个很难通过其他方法找到的解决方案，这是通过其他方法来证明这一点的。
This is the third in a series of papers which outlines an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via the study of their Coulomb branch geometries. Here we use the fact that the encoding of a Coulomb branch geometry as a Seiberg-Witten curve and 1-form enjoys a large reparametrisation invariance. While there is always a unique way to fix this invariance such that the curve and 1-form are single-valued over the Coulomb branch -- the "canonical frame" of the curve used in the first two papers in this series -- there are other useful frames in which the curve is single-valued but the 1-form is allowed to be multi-valued. In these frames, which we call "automorphism frames", the 1-form is periodic up to an automorphism twist. We argue that the multi-valuedness of the automorphism frame can simplify the computational complexity of finding new consistent scale invariant solutions. We demonstrate this in an example by using the automorphism frame to construct for the first time a genus 2 Seiberg-Witten curve for the $\mathcal{N}{=}4$ SU(3) superYang-Mills theory, a solution that is hard to find by other approaches.
