Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-08
Nucl.Phys. B711 (2005) 409-479
Physics
High Energy Physics
High Energy Physics - Theory
73 pages, plain Tex, uses harvmac, version 2, extra references
Scientific paper
10.1016/j.nuclphysb.2005.01.013
Superconformal Ward identities are derived for the the four point functions of chiral primary BPS operators for $\N=2,4$ superconformal symmetry in four dimensions. Manipulations of arbitrary tensorial fields are simplified by introducing a null vector so that the four point functions depend on two internal $R$-symmetry invariants as well as two conformal invariants. The solutions of these identities are interpreted in terms of the operator product expansion and are shown to accommodate long supermultiplets with free scale dimensions and also short and semi-short multiplets with protected dimensions. The decomposition into $R$-symmetry representations is achieved by an expansion in terms of two variable harmonic polynomials which can be expressed also in terms of Legendre polynomials. Crossing symmetry conditions on the four point functions are also discussed.
Nirschl M.
Osborn Herbert
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