Abstract
We study the unflavored Schur indices in the \( \mathcal{N} \) = 4 super-Yang-Mills theory for the Bn, Cn, Dn, G2 gauge groups. We explore two methods, namely the character expansion method and the Fermi gas method, to efficiently compute the q-series expansion of the Schur indices to some high orders. Using the available data and the modular properties, we are able to fix the exact formulas for the general gauge groups up to some high ranks and discover some interesting new features. We also identify some empirical modular anomaly equations, but unlike the case of An groups, they are quite complicated and not sufficiently useful to fix exact formulas for gauge groups of arbitrary rank.
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Acknowledgments
We thank Sheldon Katz, Albrecht Klemm for stimulating collaborations on related papers and Jun-Hao Li, Gao-fu Ren, Pei-xuan Zeng for helpful discussions. XW thanks Tadashi Okazaki and Yongchao Lü for helpful discussions. BD and MH thank Chiung Hwang, Sung-Soo Kim, Yiwen Pan, Futoshi Yagi, Wenbin Yan for related enlightening lectures at the PCFT (Peng Huanwu Center for Fundamental Theory) mini advanced school “Supersymmetric field theories and related topics” in August 2023. The works of MH was supported in parts by National Natural Science Foundation of China (Grant No. 12247103). XW is supported by a KIAS Individual Grant QP079201.
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Du, Bn., Huang, Mx. & Wang, X. Schur indices for \( \mathcal{N} \) = 4 super-Yang-Mills with more general gauge groups. J. High Energ. Phys. 2024, 9 (2024). https://doi.org/10.1007/JHEP03(2024)009
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DOI: https://doi.org/10.1007/JHEP03(2024)009