Correlators of Short Multi-Trace Operators in N=4 Supersymmetric Yang-Mills

TL;DR

The paper proves that two- and three-point functions of short multi-trace operators in ${ m N}=4$ SYM, transforming in the $(0,k,0)$ representation of $SU(4)_R$, do not receive radiative corrections at order $g^2$ for any gauge group. By adapting the perturbative framework used for single-trace short multiplets and employing color-trace identities, it shows cancellations of $O(g^2)$ contributions from self-energy and four-point interactions, extending non-renormalization to the multi-trace sector. A general three-point function is addressed in the Appendix, reinforcing the claim that these correlators are protected by ${ m N}=4$ superconformal symmetry, potentially via Ward identities and the bonus ${U(1)}_Y$ symmetry. The results support a broader non-renormalization structure in ${ m N}=4$ SYM, with implications for AdS/CFT correspondence and the organization of operator states beyond leading $N$.

Abstract

Multi-trace scalar operators in the (0,k,0) representations of SU(4)_R share many properties with their single-trace analogs. These multi-trace operators are primary fields of short representations of the N=4 superconformal group. Thus, they have protected dimensions. We show that two- and three-point correlator functions of such operators do not receive radiative corrections at order g^2 in perturbation theory for an arbitrary gauge group.