Exceptional non-renormalization properties and OPE analysis of chiral four-point functions in N=4 SYM_4

TL;DR

The paper investigates non-renormalization properties in ${\cal N}=4$ SYM$_4$ by exploiting a partial non-renormalization theorem for four-point functions of chiral primary operators and performing a conformal partial wave analysis (CPWA). It develops a series and analytic-regularization framework for the two-loop ($O(\lambda^2)$) four-point function, enabling precise OPE matching. The authors identify non-renormalized operators in the ${\bf 20}$ and ${\bf 105}$ representations and compute two-loop anomalous dimensions for Konishi-sector multiplets, while revealing a non-renormalized dimension-6 scalar $O_{6,0}$ and operator-splitting phenomena. These results deepen the understanding of dynamical non-renormalization and operator mixing in ${\cal N}=4$ SYM$_4$, with implications for AdS/CFT checks and the structure of the operator algebra.

Abstract

We show that certain classes of apparently unprotected operators in N=4 SYM_4 do not receive quantum corrections as a consequence of a partial non-renormalization theorem for the 4-point function of chiral primary operators. We develop techniques yielding the asymptotic expansion of the 4-point function of CPOs up to order O(λ^2) and we perform a detailed OPE analysis. Our results reveal the existence of new non-renormalized operators of approximate dimension 6.

Figures (1)

• Figure 1: Regularized ladder diagram related to the function $\Phi^{(2)}(v,y)$.