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

Understand

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.