Superconformal operators in N=4 super-Yang-Mills theory

TL;DR

This paper constructs supermultiplets of twist-two conformal operators in N=4 super-Yang-Mills theory, revealing their integrable structure and unified supermultiplet organization, which extends known QCD results.

Contribution

It introduces a supermultiplet framework for twist-two operators in N=4 SYM and links their renormalization to integrable spin chain models, extending previous QCD findings.

Findings

All quasipartonic operators with different SU(4) quantum numbers form a single supermultiplet.

The one-loop dilatation operator matches an integrable SL(2|4) Heisenberg spin chain.

The supermultiplet structure unifies operators of maximal helicity and other sectors.

Abstract

We construct, in the framework of the N=4 SYM theory, a supermultiplet of twist-two conformal operators and study their renormalization properties. The components of the supermultiplet have the same anomalous dimension and enter as building blocks into multi-particle quasipartonic operators. The latter are determined by the condition that their twist equals the number of elementary constituent fields from which they are built. A unique feature of the N=4 SYM is that all quasipartonic operators with different SU(4) quantum numbers fall into a single supermultiplet. Among them there is a subsector of the operators of maximal helicity, which has been known to be integrable in the multi-color limit in QCD, independent of the presence of supersymmetry. In the N=4 SYM theory, this symmetry is extended to the whole supermultiplet of quasipartonic operators and the one-loop dilatation operator coincides with a Hamiltonian of integrable SL(2|4) Heisenberg spin chain.