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Abstract: We derive a product rule satisfied by restricted Schur polynomials. We focusmostly on the case that the restricted Schur polynomial is built using twomatrices, although our analysis easily extends to more than two matrices. Thisproduct rule allows us to compute exact multi-point correlation functions ofrestricted Schur polynomials, in the free field theory limit. As an example ofthe use of our formulas, we compute two point functions of certain single traceoperators built using two matrices and three point functions of certainrestricted Schur polynomials, exactly, in the free field theory limit. Ourresults suggest that gravitons become strongly coupled at sufficiently highenergy, while the restricted Schur polynomials for totally antisymmetricrepresentations remain weakly interacting at these energies. This is in perfectaccord with the half-BPS single matrix results of hep-th-0512312. Finally, bystudying the interaction of two restricted Schur polynomials we suggest aphysical interpretation for the labels of the restricted Schur polynomial: thecomposite operator $\chi {R,r n,r m}Z,X$ is constructed from the half BPS``partons- $\chi {r n}Z$ and $\chi {r m}X$.

Autor: Rajsekhar Bhattacharyya, Robert de Mello Koch, Michael Stephanou

Fuente: https://arxiv.org/


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