Abstract
We study generating functions of \( \frac{1}{4} \)-BPS states in \( \mathcal{N} \) = 4 super Yang-Mills at finite N by attempting to generalize the Harish-Chandra-Itzykson-Zuber integral to multiple commuting matrices. This allows us to compute the overlaps of two or more generating functions; such calculations arise in the computation of two-point correlators in the free-field limit. We discuss the four-matrix HCIZ integral in the U(2) context and lay out a prescription for finding a more general formula for N > 2. We then discuss its connections with the restricted Schur polynomial operator basis. Our results generalize readily to arbitrary numbers of matrices, opening up the opportunity to study more generic BPS operators.
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Acknowledgments
We would like to thank D. Berenstein for helpful discussions. A.H. would like to thank the organizers of the Physics Summer workshop at the Simons Center for Geometry and Physics for their hospitality. SW’s research was supported in part by the Department of Energy under grant DE-SC0019139.
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Holguin, A., Wang, S. & Wang, ZY. Multi-matrix correlators and localization. J. High Energ. Phys. 2024, 30 (2024). https://doi.org/10.1007/JHEP04(2024)030
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DOI: https://doi.org/10.1007/JHEP04(2024)030