Nilpotent invariants in N=4 SYM

TL;DR

This paper investigates the existence of nilpotent invariants in N=4 SYM superspace, revealing their absence for up to four points and the presence of a non-invariant five-point invariant, impacting correlation function behaviors.

Contribution

It demonstrates the non-existence of nilpotent invariants for n≤4 points and identifies a five-point invariant not invariant under U(1)_Y, clarifying correlation function properties.

Findings

No nilpotent invariants for n≤4 points

Existence of a five-point invariant not U(1)_Y invariant

Two- and three-point functions are tree-level exact

Abstract

It is shown that there are no nilpotent invariants in N=4 analytic superspace for $n\leq4$ points. It is argued that there is (at least) one such invariant for n=5 points which is not invariant under U(1)_Y. The consequences of these results are that the n=2 and 3 point correlation functions of the N=4 gauge-invariant operators which correspond to KK multiplets in AdS supergravity are given exactly by their tree level expressions, the 4 point correlation functions of such operators are invariant under U(1)_Y and correlation functions with $n\geq 4$ points have non-trivial dependence on the Yang-Mills coupling constant.