Nesting and Dressing

Details Nesting and Dressing Nesting and Dressing

2007-02-19

arxiv.org/abs/hep-th/0702151v2

J.Stat.Mech.0708:P08006,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, 2 figures. v2: References and appendix discussing the emulation of the dressing phase added

Scientific paper

10.1088/1742-5468/2007/08/P08006

We compute the anomalous dimensions of field strength operators Tr F^L in N=4 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, respectively, 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 so(6) singlet state.

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