The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector

TL;DR

This paper derives the two-loop dilatation operator for the scalar SO(6) sector in planar N=4 super Yang-Mills theory, providing a detailed spin-chain Hamiltonian and insights into three-point functions.

Contribution

It presents the explicit form of the two-loop dilatation operator in the SO(6) sector, including new coefficients determined through diagrammatic methods and representation theory.

Findings

Derived the two-loop dilatation operator for the SO(6) sector.

Identified four coefficients from known sectors and determined four new ones.

Discussed implications for three-point structure functions at one-loop.

Abstract

The dilatation operator of planar N=4 super Yang-Mills in the pure scalar SO(6) sector is derived at the two-loop order. Representation theory allows for eight free coefficients in an ansatz for the corresponding spin-chain hamiltonian acting on three adjacent scalar states. While four out of these follow from the known SU(2|3) sector two-loop dilatation operator, the remaining four coefficients are derived by diagrammatic techniques and a match to the known dimension of a length three primary operator. Finally, comments upon the use of this result for the evaluation of three-point structure functions of scalar operators at the one-loop order are given.