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

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 Sn. 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 AdS5 × S spacetime to gauge invariant operators of the dual N = 4 SYM. E-mail address: [email protected] E-mail address: [email protected] E-mail address: [email protected]