论文标题
3d $ {\ cal n} = 4 $量规理论的非扰动Schwinger-Dyson方程
Non-Perturbative Schwinger-Dyson Equations for 3d ${\cal N} = 4$ Gauge Theories
论文作者
论文摘要
我们分析了对应于3d $ {\ cal} n = 4 $仪表理论的分离的拓扑领域的对称性，并用希格斯真空吸真空层，并在一个圆上压实。对称性是在通过某个规格不变的操作员“涡旋字符”的相关函数满足的施温格 - 迪森身份中编码的。在存在1/2-BPS线缺陷的情况下，这种观察到的特征可被实现为3D量规理论的涡流分区函数。该角色享有双重精致，被解释为量子仿射代数有限维表示的通常特征的变形。我们从各种物理角度来得出3D理论的Schwinger-dyson身份：在3D仪表理论本身中，用一维量子力学，2d $ q $ -toda理论和6D小弦理论中的一维量子力学。我们在所有方法之间建立了词典。最后，我们在三维seiberg二元性的作用下对涡流字符的转换属性发表评论。
We analyze symmetries corresponding to separated topological sectors of 3d ${\cal} N=4$ gauge theories with Higgs vacua, compactified on a circle. The symmetries are encoded in Schwinger-Dyson identities satisfied by correlation functions of a certain gauge-invariant operator, the "vortex character." Such a character observable is realized as the vortex partition function of the 3d gauge theory, in the presence of a 1/2-BPS line defect. The character enjoys a double refinement, interpreted as a deformation of the usual characters of finite-dimensional representations of quantum affine algebras. We derive and interpret the Schwinger-Dyson identities for the 3d theory from various physical perspectives: in the 3d gauge theory itself, in a 1d gauged quantum mechanics, in 2d $q$-Toda theory, and in 6d little string theory. We establish the dictionary between all approaches. Lastly, we comment on the transformation properties of the vortex character under the action of three-dimensional Seiberg duality.
