@MISC{Rej_nestingand, author = {Adam Rej and Matthias Staudacher and Stefan Zieme}, title = {Nesting and dressing}, year = {} }

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Abstract

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 L → ∞ 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 nontrivial “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. 1 Motivation, Conclusion and Overview There is much evidence that planar N = 4 SYM theory is integrable and that its spectral problem is therefore exactly solvable. It was shown by Minahan and Zarembo that the dilatation operator in the scalar matter sector at one loop can be mapped to the Hamiltonian