Abstract
We study the large N and large representation limits of the Schur line defect correlators of the Wilson line operators transforming in the (anti)symmetric, hook and rectangular representations for 𝒩 = 4 U(N) super Yang-Mills theory. By means of the factorization property, the large N correlators of the Wilson line operators in arbitrary representations can be exactly calculated in principle. In the large representation limit they turn out to be expressible in terms of certain infinite series such as Ramanujan’s general theta functions and the q-analogues of multiple zeta values (q-MZVs). Several generating functions for combinatorial objects, including partitions with non-negative cranks and conjugacy classes of general linear groups over finite fields, emerge from the large N correlators. Also we find conjectured properties of the automorphy and the hook-length expansion satisfied by the large N correlators.
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Acknowledgments
The authors would like to thank Kimyeong Lee, Hai Lin and Masatoshi Noumi for useful discussions and comments. The work of Y.H. was supported in part by JSPS KAKENHI Grant No. 22K03641. The work of T.O. was supported by the Startup Funding no. 4007012317 of the Southeast University.
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Hatsuda, Y., Okazaki, T. Large N and large representations of Schur line defect correlators. J. High Energ. Phys. 2024, 96 (2024). https://doi.org/10.1007/JHEP01(2024)096
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DOI: https://doi.org/10.1007/JHEP01(2024)096