Superconformal Symmetry in Six-dimensions and Its Reduction to Four

TL;DR

This paper explores superconformal symmetry in six dimensions, deriving its structure, solutions, and correlation functions, and discusses its reduction to four dimensions with implications for superspace and covariant operators.

Contribution

It provides a detailed analysis of six-dimensional superconformal symmetry, including the superconformal Killing equation, solutions, and the reduction process to four dimensions.

Findings

Superconformal group in 6D is OSp(2,6|N) for N chiral supersymmetries.

Explicit formulas for two- and three-point correlation functions are given.

Reduction to 4D yields an extended superconformal group and covariant differential operators.

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|8N}. We define superinversion as a map to the associated superspace of opposite chirality. General formulae for two-point 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.