Multi-matrix correlators and localization - Adolfo Holguin; Shannon Wang; Zi-Yue Wang (Journal of High Energy Physics, 2024)
Abstract We study generating functions of 1 4 $$ \frac{1}{4} $$ -BPS states in N $$ \mathcal{N} $$ = 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.