BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations
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| Format: | Preprint |
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2017
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| _version_ | 1866916283896823808 |
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| author | Jeong, Saebyeok Zhang, Xinyu |
| author_facet | Jeong, Saebyeok Zhang, Xinyu |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1710_06970 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations Jeong, Saebyeok Zhang, Xinyu High Energy Physics - Theory 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. |
| title | BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/1710.06970 |