Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
Wrapping interactions and a new source of corrections to the spin-chain/string duality
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abstract
Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an integrable {\em quantum} field theory, we deduce that there might be new corrections to the spin-chain/string Bethe ansatz paradigm. These come from virtual particles propagating around the circumference of the cylinder and render Bethe ansatz quantization conditions only approximate. We determine the nature of these corrections both at weak and at strong coupling in the near BMN limit, and find that the first corrections behave qualitatively as wrapping interactions at weak coupling.
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Non-planar corrections lift degeneracies in the spectrum of quarter BPS states in Sym^N(T^4) and introduce level repulsion plus random matrix statistics, showing integrability is restricted to the large N planar limit.
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Positivity properties of observables in planar maximally supersymmetric Yang-Mills theory
Several observables in planar N=4 SYM, including the octagon anomalous dimension and Bremsstrahlung function, admit a once-subtracted dispersion representation over a positive measure in the coupling.
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Non-planar corrections in the symmetric orbifold
Non-planar corrections lift degeneracies in the spectrum of quarter BPS states in Sym^N(T^4) and introduce level repulsion plus random matrix statistics, showing integrability is restricted to the large N planar limit.