Diagonal multi-matrix correlators and BPS operators 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.

36+12 pages, 7 figures, typos corrected, references added

References in corpus (7)

• Branes, Anti-Branes and Brauer Algebras in Gauge-Gravity duality
• Anatomy of bubbling solutions
• Counting BPS operators in N=4 SYM
• Giant Gravitons - with Strings Attached (II)
• Bubbling AdS and droplet descriptions of BPS geometries in IIB supergravity
• N=4 Superconformal Characters and Partition Functions
• Half-BPS SU(N) Correlators in N=4 SYM

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• Schur-Weyl duality as an instrument of Gauge-String duality
• Permutations and the Loop
• Restricted Schur Polynomials and Finite N Counting
• Supergravitons from one loop perturbative N=4 SYM
• Correlators Of Operators with a Large R-charge