论文标题
作为Nekrasov微积分的隐藏起源的可整合性
Superintegrability as the hidden origin of Nekrasov calculus
论文作者
论文摘要
现在，Nekrasov功能与共同块之间的AGT关系曾经有些神秘，现在被理解为Dijkgraaf-Vafa（DV）阶段的Hubbard-Stratanovich二元性。但是，它在很大程度上仍然是一系列有些技术技巧，缺乏明确且可普遍的概念解释。我们的新主张是，Nekrasov在矩阵模型中出现了功能，这是可巩固性的直接含义，特殊矩阵模型平均分解的分解。最近，我们证明，在高斯遗产模型中，分解属性可以从单个字符的平均值扩展到其双线性组合。在本文中，我们声称这对于多层次矩阵模型也是如此，其中分解只是两个字符的点分解产物。正是这种增强的可共性导致了Nekrasov函数和AGT关系的存在。可以将此属性推广到多矩阵模型，从而导致多点共形块的AGT关系，以及其他非高斯模型的DV阶段。
Once famous and a little mysterious, AGT relations between Nekrasov functions and conformal blocks are now understood as the Hubbard-Stratanovich duality in the Dijkgraaf-Vafa (DV) phase of a peculiar Dotsenko-Fateev multi-logarithmic matrix model. However, it largely remains a collection of somewhat technical tricks, lacking a clear and generalizable conceptual interpretation. Our new claim is that the Nekrasov functions emerge in matrix models as a straightforward implication of superintegrability, factorization of peculiar matrix model averages. Recently, we demonstrated that, in the Gaussian Hermitian model, the factorization property can be extended from averages of single characters to their bilinear combinations. In this paper, we claim that this is true also for multi-logarithmic matrix models, where factorized are just the point-split products of two characters. It is this enhanced superintegrability that is responsible for existence of the Nekrasov functions and the AGT relations. This property can be generalized both to multi-matrix models, thus leading to AGT relations for multi-point conformal blocks, and to DV phases of other non-Gaussian models.
