Non-Perturbative Green's Functions in Theories with Extended Superconformal Symmetry

TL;DR

This paper explores the constraints imposed by superconformal symmetry on Green's functions in four-dimensional supersymmetric theories, revealing the absence of chiral invariants and restrictions on analytic operator correlators.

Contribution

It derives superconformal Ward identities for Green's functions and demonstrates the non-existence of chiral superconformal invariants in these theories.

Findings

No chiral superconformal invariants exist.

Superconformal Ward identities severely restrict analytic Green's functions.

Analytic operator Green's functions are highly constrained by symmetry.

Abstract

The multiplets that occur in four dimensional rigidly supersymmetric theories can be described either by chiral superfields in Minkowski superspace or analytic superfields in harmonic superspace. The superconformal Ward identities for Green's functions of gauge invariant operators of these types are derived. It is shown that there are no chiral superconformal invariants. It is further shown that the Green's functions of analytic operators are severely restricted by the superconformal Ward when analyticity is taken into account.