Multi-matrix correlators and localization

Abstract

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.

Keywords

• AdS-CFT Correspondence
• D-Branes
• Matrix Models
• Supersymmetric Gauge Theory