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

作者：Leurent Sebastien^*; Volin Dmytro

来源：Nuclear Physics B, 2013, 875(3): 757-789.

DOI：10.1016/j.nuclphysb.2013.07.020

• Y-system
• FiNLIE
• Integrability
• Perturbative quantum field theory
• AdS/CFT correspondence

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. %26lt;br%26gt;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 non-trivial at double wrapping.

• 出版日期2013-10-21