arXiv 2009.089892020-09hep-thmath-phmath.MPmath.QA

三维${\cal N} = 4$规范理论的非微扰Schwinger-Dyson方程

Non-Perturbative Schwinger-Dyson Equations for 3d ${\cal N} = 4$ Gauge Theories

Nathan Haouzi

备注：: 73 pages; 12 figures; v2: corrected various typos in text and figures, discussion of Wilson loops is removed for clarity v3: added references and made Section 6 slightly clearer

摘要：

我们分析了对称性对应的三维${\cal} N=4$规范理论与希格斯真空，在一个圆上紧化分离的拓扑扇区。这些对称性被编码在Schwinger-Dyson恒等式中，该恒等式由特定规范不变算子的关联函数所满足，即“涡旋特征”。“在存在1/2 BPS线缺陷的情况下，这样一个可观测的特征被实现为三维规范理论的涡旋配分函数。字符享有双重细化，解释为变形的量子仿射代数的有限维表示的通常字符。我们从不同的物理角度推导和解释了3d理论的Schwinger-Dyson恒等式：在3d规范理论本身中，在1d规范量子力学中，在2d $q$ -Toda理论中，以及在6d小弦论中。我们建立了所有方法之间的字典。最后，我们讨论了涡旋特征标在三维Seiberg对偶作用下的变换性质。

英文摘要：

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.

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摘要：

英文摘要：

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