Explicit construction of nilpotent covariants in N=4 SYM

TL;DR

The paper investigates how contact covariants and nilpotent superconformal structures in N=4 SYM influence non-renormalisation theorems. It uses $N=4$ analytic and $N=2$ harmonic superspace to classify contact covariants and derives the reduction formula that links n-point and (n+1)-point functions. A central result is a two-loop, five-point calculation in $N=2$ harmonic superspace that reproduces the coupling-derivative of a four-point function and explicitly constructs a five-point nilpotent covariant violating $U(1)_Y$, supporting the existence of such invariants and showing contact terms do not affect the reduction framework. The findings also yield simplifications in computing higher-point correlators and reinforce the consistency of the $N=4$ harmonic-superspace approach with known N=4 SYM correlators.

Abstract

Some aspects of correlation functions in N=4 SYM are discussed. Using N=4 harmonic superspace we study two and three-point correlation functions which are of contact type and argue that these contact terms will not affect the non-renormalisation theorem for such correlators at non-coincident points. We then present a perturbative calculation of a five-point function at two loops in N=2 harmonic superspace and verify that it reproduces the derivative of the previously found four-point function with respect to the coupling. The calculation of this four-point function via the five-point function turns out to be significantly simpler than the original direct calculation. This calculation also provides an explicit construction of an N=2 component of an N=4 five-point nilpotent covariant that violates U(1)_Y symmetry.