OPEs and 3-point correlators of protected operators in N=4 SYM

TL;DR

This work develops a comprehensive analytic-superspace framework for $N=4$ SYM to compute and constrain two- and three-point functions of protected operators and their OPEs. By realizing all relevant superconformal representations as analytic superfields on $(4,2,2)$, it derives explicit formulae for two- and three-point correlators, classifies protected versus unprotected operators via integral versus non-integral Dynkin labels, and shows $U(1)_Y$ invariance underpinning non-renormalisation for $n\le4$ correlators. The introduction of quasi-tensor superfields enables the inclusion of unprotected operators and anomalous dimensions within a consistent analytic framework, and extremal correlators are shown to retain a non-renormalised, factorised structure; the results point to broad applicability of analytic superspace methods to higher-point functions and other SCFTs across dimensions.

Abstract

Two- and three-point correlation functions of arbitrary protected operators are constructed in N=4 SYM using analytic superspace methods. The OPEs of two chiral primary multiplets are given. It is shown that the $n$-point functions of protected operators for $n\leq4$ are invariant under $U(1)_Y$ and it is argued that this implies that the two- and three-point functions are not renormalised. It is shown explicitly how unprotected operators can be accommodated in the analytic superspace formalism in a way which is fully compatible with analyticity. Some new extremal correlators are exhibited.