Superconformal Invariants and Extended Supersymmetry

TL;DR

This paper identifies superconformal invariants in analytic superspace and demonstrates their implications for the invariance and evaluation of Green's functions in N=2 and N=4 supersymmetric Yang-Mills theories.

Contribution

It introduces superconformal invariants in analytic superspace and links invariance to the structure of Green's functions, enabling their evaluation in certain supersymmetric gauge theories.

Findings

Superconformal invariants are explicitly constructed in analytic superspace.

Green's functions are shown to be invariant holomorphic sections of line bundles.

Correlation functions for low-dimension operators can be computed up to constants.

Abstract

The superconformal invariants in analytic superspace are found. Superconformal invariance is shown to imply that the Green's functions of analytic operators are invariant holomorphic sections of a line bundle on a product of certain harmonic superspaces. It is argued that the correlation functions for a class of sufficiently low dimension gauge invariant operators in N=2 and N=4 supersymmetric Yang-Mills theory can be evaluated up to constants.