Multiple zeta functions and double wrapping in planar N=4 SYM
2013 (English)In: Nuclear Physics B, ISSN 0550-3213, Vol. 875, no 3, 757-789 p.Article in journal (Refereed) Published
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 non-trivial at double wrapping.
Place, publisher, year, edition, pages
2013. Vol. 875, no 3, 757-789 p.
Y-system, FiNLIE, Integrability, Perturbative quantum field theory, AdS/CFT correspondence
IdentifiersURN: urn:nbn:se:kth:diva-131706DOI: 10.1016/j.nuclphysb.2013.07.020ISI: 000324601700011ScopusID: 2-s2.0-84883187860OAI: oai:DiVA.org:kth-131706DiVA: diva2:657222
FunderEU, European Research Council, 290456
QC 201310182013-10-182013-10-172013-10-18Bibliographically approved