Defects, modular differential equations, and free field realization of N=4 vertex operator algebras

作者：Yiwen Pan, Yufan Wang, Haocong Zheng · 发表于：Physical review. D/Physical review. D. · 年份：2022 · DOI：10.1103/physrevd.105.085005 · 被引用次数：12 · 研究领域：Algebraic structures and combinatorial models、Black Holes and Theoretical Physics、Physics of Superconductivity and Magnetism

For all 4D $\mathcal{N}=4$ Super-Yang-Mills theories with simple gauge groups $G$, we show that a set of 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 $\mathrm{rank}G$ copies of $bc\ensuremath{\beta}\ensuremath{\gamma}$ systems that provide the free field realization of associated $\mathcal{N}=4$ vertex operator algebras in [F. Bonetti, C. Meneghelli, and L. Rastelli, J. High Energy Phys. 05 (2019) 155]. 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.