Integrability in Yang-Mills theory on the light cone beyond leading order

TL;DR

This paper investigates the persistence of integrability in Yang-Mills theory beyond leading order, revealing that it survives in certain supersymmetric cases but is broken in others, through two-loop dilatation operator calculations.

Contribution

It extends the understanding of integrability in Yang-Mills theories by calculating two-loop corrections and identifying conditions under which integrability persists or breaks.

Findings

Integrability survives in adjoint matter for SU(N_c) gauge groups.

Integrability is broken for matter in the fundamental representation.

Supersymmetric theories N=1, N=2, N=4 retain integrability at two loops.

Abstract

The one-loop dilatation operator in Yang-Mills theory possesses a hidden integrability symmetry in the sector of maximal helicity Wilson operators. We calculate two-loop corrections to the dilatation operator and demonstrate that while integrability is broken for matter in the fundamental representation of the SU(3) gauge group, for the adjoint SU(N_c) matter it survives the conformal symmetry breaking and persists in supersymmetric N=1, N=2 and N=4 Yang-Mills theories.