Analytic three-loop solutions for SYM twist operators

We introduce a method to obtain the analytic solution of the higher-order Baxter equation for twist-two and twist-three operators of planar N = 4 SYM. Our result proofs the conjectured formula for the threeloop anomalous dimension of twist-two operators. As such we derive the maximally transcendental part of the corresponding three-loop QCD result from the maximal supersymmetric gauge theory in four dimension purely by methods of integrability. © 2009 Elsevier B.V. All rights reserved.