2005/11/30 by Benjamin I. Zwiebel, Benjamin I Zwiebel · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/02/055
published as JHEP0602:055,2006 · 28 pages, v2: additional checks against direct field theory calculations, references added, minor corrections, v3: additional minor corrections
openalex publication_date 2006/02/22 · arxiv created 2006/03/15 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/29
We begin a study of higher-loop corrections to the dilatation generator of N=4 SYM in non-compact sectors. In these sectors, the dilatation generator contains infinitely many interactions, and therefore one expects very complicated higher-loop corrections. Remarkably, we find a short and simple expression for the two-loop dilatation generator. Our solution for the non-compact su(1,1|2) sector consists of nested commutators of four O(g) generators and one simple auxiliary generator. Moreover, the solution does not require the planar limit; we conjecture that it is valid for any gauge group. To obtain the two-loop dilatation generator, we find the complete O(g3) symmetry algebra for this sector, which is also given by concise expressions. We check our solution using published results of direct field theory calculations. By applying the expression for the two-loop dilatation generator to compute selected anomalous dimensions and the bosonic sl(2) sector internal S-matrix, we confirm recent conjectures of the higher-loop Bethe ansatz of hep-th/0412188.