Superconformal Symmetry and Correlation Functions

TL;DR

This paper investigates four-dimensional superconformal symmetry and correlation functions of superfields, deriving invariants and general forms of n-point functions, with implications for N=4 super Yang-Mills theory and AdS/CFT correspondence.

Contribution

It provides a classification of superconformal Killing equations, identifies all superconformal invariants, and derives the general form of n-point functions for scalar superfields in superspace.

Findings

Superconformal invariants are explicitly identified.

General form of n-point functions for scalar superfields is derived.

A selection rule for correlation functions in N=4 super Yang-Mills is established.

Abstract

Four-dimensional N-extended superconformal symmetry and correlation functions of quasi-primary superfields are studied within the superspace formalism. A superconformal Killing equation is derived and its solutions are classified in terms of supertranslations, dilations, Lorentz transformations, R-symmetry transformations and special superconformal transformations. In general, due to the invariance under supertranslations and special superconformal transformations, superconformally invariant n-point functions reduce to one unspecified (n-2)-point function which must transform homogeneously under the remaining rigid transformations, i.e. dilations, Lorentz transformations and R-symmetry transformations. Based on this result, we are able to identify all the superconformal invariants and obtain the general form of n-point functions for scalar superfields. In particular, as a byproduct, a selection rule for correlation functions is derived, the existence of which in N=4 super Yang-Mills theory was previously predicted in the context of AdS/CFT correspondence. Superconformally covariant differential operators are also discussed.