论文标题
$ tt^*$ toda方程的表面缺陷中的$ {\ Mathcal n} = 2 $ sym和Instanton计数经典谎言组
$tt^*$ Toda equations for surface defects in ${\mathcal N}=2$ SYM and instanton counting for classical Lie groups
论文作者
论文摘要
$ \ Mathcal {n} = 2 $ Super Yang-Mills理论的分区功能与自dual $ω$ - background结合使用任意简单量规组，这表明可以通过研究与表面操作员产生其单一形式符号的表面操作员相关的重新分配组方程来完全确定。相应的方程式系统导致$ {\ it非自主} $ toda链在兰兰兹双重的根系上，演变参数为RG量表。一个系统的算法计算完整的多内斯顿校正是根据递归关系得出的，其规范理论解决方案仅通过固定IR前稳态的扰动部分作为其RGE的渐近边界条件而获得。我们分析了$τ$系统的明确解决方案，以在各种层面上为所有古典群体分析，将分析扩展到仿射扭曲的谎言代数，并为线性Quiver Gauge理论的$τ$功能提供猜想的双线关系。
The partition function of $\mathcal{N}=2$ super Yang-Mills theories with arbitrary simple gauge group coupled to a self-dual $Ω$-background is shown to be fully determined by studying the renormalization group equations relevant to the surface operators generating its one-form symmetries. The corresponding system of equations results in a ${\it non-autonomous}$ Toda chain on the root system of the Langlands dual, the evolution parameter being the RG scale. A systematic algorithm computing the full multi-instanton corrections is derived in terms of recursion relations whose gauge theoretical solution is obtained just by fixing the perturbative part of the IR prepotential as its asymptotic boundary condition for the RGE. We analyse the explicit solutions of the $τ$-system for all the classical groups at the diverse levels, extend our analysis to affine twisted Lie algebras and provide conjectural bilinear relations for the $τ$-functions of linear quiver gauge theory.
