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

TL;DR

This work investigates whether two- and three-point correlators of gauge-invariant operators in ${\cal N}=4$ SYM receive ${\cal O}(g_{YM}^2)$ corrections. It employs ${\cal N}=1$ superspace to compute these correlators via the effective action $S_{eff}(J)$, enabling direct extraction of descendent correlators. The key finding is that all corrections are contact terms that vanish for separated points, in agreement with non-renormalization theorems and consistent with ${\cal N}=4$ supersymmetry, even though the calculation uses ${\cal N}=1$ formalism; gauge-choice independence is shown by matching results across gauges. This validates the robustness of protected correlators and demonstrates the practicality of ${\cal N}=1$ superspace for probing component-level constraints in ${\cal N}=4$ SYM.

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 $þ$-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.