Superconformal symmetry in six dimensions and its reduction to four

Abstract

Superconformal symmetry in six dimensions is analyzed in terms of coordinate transformations on superspace. A superconformal Killing equation is derived and its solutions are identified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. The full superconformal symmetry, which is shown to form the group OSp(2, 6| N), is possible only if the supersymmetry algebra has N spinorial generators of the same chirality, corresponding to ( N,0) supersymmetry. The R-symmetry group is then Sp( N) and the corresponding superspace is R 6/vb8n . We define superinversion as a map to the associated superspace of opposite chirality. General formulae for two- and three-point correlation functions of quasi-primary superfields are exhibited. The superconformal group in six dimensions is reduced to a corresponding extended superconformal group in four dimensions. Superconformally covariant differential operators are also discussed.