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Multiple zeta functions and double wrapping in planar N=4 SYM
Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
2013 (English)In: Nuclear Physics B, ISSN 0550-3213, Vol. 875, no 3, 757-789 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Y-system, FiNLIE, Integrability, Perturbative quantum field theory, AdS/CFT correspondence
National Category
Physical Sciences
URN: urn:nbn:se:su:diva-95074DOI: 10.1016/j.nuclphysb.2013.07.020ISI: 000324601700011OAI: diva2:658726



Funding Agency:

ERC 290456 

Available from: 2013-10-22 Created: 2013-10-21 Last updated: 2013-10-22Bibliographically approved

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