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arXiv 1710.06970hep-th
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高阶退化场的BPZ方程与非微扰Dyson-Schwinger方程

BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations

Saebyeok Jeong, Xinyu Zhang

备注：
23 pages; v2: additional references and minor corrections; v3: minor corrections, published in PRD
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AI总结：

本文证明二维Liouville共形场论中高阶退化场满足的BPZ方程与四维N=2超对称理论瞬子配分函数由非微扰Dyson-Schwinger方程导出的偏微分方程在次最简单情形下相互等同，从而验证了BPS/CFT对应。

摘要：

在二维Liouville共形场论中，涉及退化场的关联函数由于零后代场的退耦而满足偏微分方程。另一方面，四维$\mathcal{N}=2$超对称理论在$Ω$-背景参数空间特殊点处的瞬子配分函数，也因规范场构型的约束而满足一个偏微分方程。该偏微分方程可以利用非微扰Dyson-Schwinger方程加以证明。我们针对次最简单情形证明，从这两种不同视角得到的偏微分方程可以相互等同，从而证实了BPS/CFT对应的一个论断。

英文摘要：

In the two-dimensional Liouville conformal field theory, correlation functions involving a degenerate field satisfy partial differential equations due to the decoupling of the null descendant field. On the other hand, the instanton partition function of a four-dimensional $\mathcal{N}=2$ supersymmetric theory in the $Ω$-background at a special point of the parameter space also satisfies a partial differential equation resulting from the constraints of the gauge field configurations. This partial differential equation can be proved using the nonperturbative Dyson-Schwinger equations. We show for the next-to-simplest case that the partial differential equations obtained from two different perspectives can be identified, thereby confirming an assertion of the BPS/CFT correspondence.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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