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arXiv · 1710.06970

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

Saebyeok Jeong·Xinyu Zhang
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Abstract

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 $\Omega$-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.

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Saebyeok Jeong, Xinyu Zhang. 2017-10-19. BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations. https://arxiv.org/abs/1710.06970

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