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Multi-matrix correlators and localization

Journal of High Energy Physics, ISSN: 1029-8479, Vol: 2024, Issue: 4
2024
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We study generating functions of 14-BPS states in 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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