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arXiv · 2104.12180

Defects, modular differential equations, and free field realization of N = 4 VOAs

Yiwen Pan·Yufan Wang·Haocong Zheng
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Abstract

For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we show that the residues of the integrands in the $\mathcal{N} = 4$ Schur indices, which are related to Gukov-Witten type surface defects in the theories, equal the vacuum characters of rank$G$ copies of $bc \beta \gamma$ systems that provide the free field realization of associated $\mathcal{N} = 4$ VOAs. This result predicts that these residues, as module characters, are additional solutions to the flavored modular differential equations satisfied by the original Schur index. The prediction is verified in the $G = SU(2)$ case, where an additional logarithmic solution is constructed.

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Yiwen Pan, Yufan Wang, Haocong Zheng. 2021-04-25. Defects, modular differential equations, and free field realization of N = 4 VOAs. https://doi.org/10.1103/physrevd.105.085005

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