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Multiple zeta functions and double wrapping in planar N=4SYM

Sébastien Leurent
Organization: Imperial College, South Kensington Campus, London
Department: Theoretical Physics group
Dmytro Volin
Organization: Bogolyubov Institute for Theoretical Physics
Journal / Anthology

Nuclear Physics B
Year: 2013
Volume: 875
Issue: 3
Page range: 757-789

Using the FiNLIE solution of the AdS/CFT Y-system, we compute the anomalous dimension of the Konishi operator in planar N=4 SYM up to eight loops, i.e. up to the leading double wrapping order. At this order a non reducible Euler-Zagier sum, zeta(1,2,8), appears for the first time. We find that at all orders in perturbation, every spectral-dependent quantity of the Y-system is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of Euler-Zagier sums. Furthermore, we conjecture that only Euler-Zagier sums can appear in the answer for the anomalous dimension at any order in perturbation theory. We also resum the leading transcendentality terms of the anomalous dimension at all orders, obtaining a simple result in terms of Bessel functions. Finally, we demonstrate that exact Bethe equations should be related to an absence of poles condition that becomes especially nontrivial at double wrapping.

*Science > Physics > Nuclear and Particle Physics