From counting to construction of BPS states in N=4 SYM

Details From counting to construction of BPS states in N=4 SYM From counting to construction of BPS states in N=4 SYM

2010-10-08

arxiv.org/abs/1010.1683v2

JHEP 1102:078,2011

Physics

High Energy Physics

High Energy Physics - Theory

41 pages + Appendices, 4 figures; v2 - refs and acknowledgments added

Scientific paper

10.1007/JHEP02(2011)078

We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry group. A related projector acting on the Hilbert space of the free theory is used to construct the matrix of two-point functions of the states annihilated by the one-loop dilatation operator, at finite N or in the large N limit. The matrix is given simply in terms of Clebsch-Gordan coefficients of symmetric groups and dimensions of U(N) representations. It is expected, by non-renormalization theorems, to contain observables at strong coupling. Using the stringy exclusion principle, we interpret a class of its eigenvalues and eigenvectors in terms of giant gravitons. We also give a formula for the action of the one-loop dilatation operator on the orthogonal basis of the free theory, which is manifestly covariant under the global symmetry.

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