Explicit construction of nilpotent covariants in N=4 SYM

TL;DR

This paper investigates correlation functions in N=4 SYM using harmonic superspace, demonstrating contact terms' non-impact on non-renormalisation and explicitly constructing a nilpotent covariant that breaks U(1)_Y symmetry.

Contribution

It provides an explicit construction of a nilpotent covariant in N=4 SYM and simplifies the calculation of four-point functions via five-point functions.

Findings

Contact terms do not affect non-renormalisation theorems at non-coincident points.

A two-loop five-point function reproduces the derivative of a four-point function.

Explicit construction of a U(1)_Y symmetry-violating nilpotent covariant.

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.