Diagonal multi-matrix correlators and BPS operators in N=4 SYM

TL;DR

This paper develops a complete basis of multi-trace multi-matrix operators with diagonal two-point functions in free N=4 SYM, enabling better understanding of BPS operators and their duals in AdS/CFT correspondence.

Contribution

It introduces a new diagonalization method for multi-matrix operators using symmetric group Clebsch-Gordan coefficients, generalizing Schur polynomial techniques to multiple matrices.

Findings

Diagonal basis for multi-matrix operators at finite N.

Framework for comparing BPS giant gravitons to gauge operators.

Enhanced understanding of operator metrics in N=4 SYM.

Abstract

We present a complete basis of multi-trace multi-matrix operators that has a diagonal two point function for the free matrix field theory at finite N. This generalises to multiple matrices the single matrix diagonalisation by Schur polynomials. Crucially, it involves intertwining the gauge group U(N) and the global symmetry group U(M) with Clebsch-Gordan coefficients of symmetric groups S_n. When applied to N=4 super Yang-Mills we consider the U(3) subgroup of the full symmetry group. The diagonalisation allows the description of a dual basis to multi-traces, which permits the characterisation of the metric on operators transforming in short representations at weak coupling. This gives a framework for the comparison of quarter and eighth-BPS giant gravitons of AdS_5 x S^5 spacetime to gauge invariant operators of the dual N=4 SYM.