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Computing ThreePoint Functions for Short Operators
"... We compute the threepoint structure constants for short primary operators of N = 4 super Yang–Mills theory to leading order in 1/ λ by mapping the problem to a flatspace string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We ..."
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We compute the threepoint structure constants for short primary operators of N = 4 super Yang–Mills theory to leading order in 1/ λ by mapping the problem to a flatspace string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the threepoint functions for any combination of chiral and nonchiral primaries, with the nonchiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role. ar X iv
Yangians in Integrable Field Theories, Spin Chains and GaugeString Dualities
 REVIEWS IN MATHEMATICAL PHYSICS
, 2012
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Multiple zeta functions and double wrapping in planar N = 4 SYM
, 2013
"... Using the FiNLIE solution of the AdS/CFT Ysystem, 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 nonreducible EulerZagier sum, ζ1,2,8, appears for the first time. We find that at all ord ..."
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Using the FiNLIE solution of the AdS/CFT Ysystem, 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 nonreducible EulerZagier sum, ζ1,2,8, appears for the first time. We find that at all orders in perturbation, every spectraldependent quantity of the Ysystem is expressed through multiple Hurwitz zeta functions, hence we provide a Mathematica package to manipulate these functions, including the particular case of EulerZagier sums. Furthermore, we conjecture that only EulerZagier 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. Keywords: Ysystem, FiNLIE, integrability, perturbative quantum field theory,