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

TL;DR

This paper demonstrates that two- and three-point correlators of multi-trace scalar operators in N=4 SYM are protected from radiative corrections at order g^2, highlighting their stability and symmetry properties.

Contribution

It establishes the non-renormalization of two- and three-point functions of multi-trace operators at order g^2 in perturbation theory, extending known results for single-trace operators.

Findings

Correlators are protected at order g^2 for arbitrary gauge groups.

Multi-trace operators share properties with single-trace operators.

Protected dimensions due to short superconformal representations.

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.