Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace

TL;DR

This paper demonstrates that certain two and three point correlators in ${ m N}=4$ SYM remain unrenormalized at order $g_{YM}^2$, confirming non-renormalization theorems using ${ m N}=1$ superspace techniques.

Contribution

It introduces a method to compute correlators in ${ m N}=1$ superspace that confirms non-renormalization of specific correlators in ${ m N}=4$ SYM.

Findings

Corrections are only contact terms, which vanish at separated points.

Results are consistent across different gauge choices.

Correlators are protected from renormalization at this order.

Abstract

Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our results show the only possible $g^2_{YM}$ corrections to the free field correlators are contact terms. Therefore they vanish for operators at separate points, verifying the known non-renormalization theorems. This also implies the results are consistent with ${\cal N}=4$ supersymmetry even though the Lagrangian we use has only ${\cal N}=1$ manifest supersymmetry. We repeat some of the calculations using supersymmetric Landau gauge and obtain, as expected, the same results as those of supersymmetric Feynman gauge.