2007/02/28 by Adam Rej, Matthias Staudacher, Stefan Zieme
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Quantum many-body systems #hep-th
paper · pdf · doi:10.1088/1742-5468/2007/08/p08006
published as J.Stat.Mech.0708:P08006,2007 · 38 pages, 2 figures. v2: References and appendix discussing the emulation of the dressing phase added
arxiv created 2007/03/26 · openalex publication_date 2007/08/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We compute the anomalous dimensions of field strength operators in super Yang–Mills theory (SYM) from an asymptotic nested Bethe ansatz to all-loop order. Starting from the exact solution of the one-loop problem at arbitrary L , we derive a single effective integral equation for the thermodynamic limit of these dimensions. We also include the recently proposed phase factor for the S -matrix of the planar AdS/CFT system. The terms in the effective equation corresponding to the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a non-trivial 'filled' structure of the theory's BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the all-loop dimension of a certain one-loop singlet state.