Abstract
The Pentagon Operator Product Expansion represents polygonal Wilson loops in planar \( \mathcal{N}=4 \) super Yang-Mills in terms of a series of flux tube excitations for finite coupling. We demonstrate how to re-sum this series at the one loop level for the hexagonal Wilson loop dual to the six-point MHV amplitude. By summing over a series of effective excitations we find expressions which integrate to logarithms and polylogarithms, reproducing the known one-loop result.
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References
B. Basso, A. Sever and P. Vieira, Spacetime and Flux Tube S-Matrices at Finite Coupling for N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 111 (2013) 091602 [arXiv:1303.1396] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data, JHEP 01 (2014) 008 [arXiv:1306.2058] [INSPIRE].
B. Basso, A. Sever and P. Vieira, Hexagonal Wilson loops in planar \( \mathcal{N}=4 \) SYM theory at finite coupling, J. Phys. A 49 (2016) 41LT01 [arXiv:1508.03045] [INSPIRE].
J.M. Drummond and G. Papathanasiou, Hexagon OPE Resummation and Multi-Regge Kinematics, JHEP 02 (2016) 185 [arXiv:1507.08982] [INSPIRE].
G. Papathanasiou, Evaluating the six-point remainder function near the collinear limit, Int. J. Mod. Phys. A 29 (2014) 1450154 [arXiv:1406.1123] [INSPIRE].
G. Papathanasiou, Hexagon Wilson Loop OPE and Harmonic Polylogarithms, JHEP 11 (2013) 150 [arXiv:1310.5735] [INSPIRE].
L. Córdova, Hexagon POPE: effective particles and tree level resummation, arXiv:1606.00423 [INSPIRE].
B. Basso, J. Caetano, L. Córdova, A. Sever and P. Vieira, OPE for all Helicity Amplitudes II. Form Factors and Data Analysis, JHEP 12 (2015) 088 [arXiv:1508.02987] [INSPIRE].
L.J. Dixon, M. von Hippel and A.J. McLeod, The four-loop six-gluon NMHV ratio function, JHEP 01 (2016) 053 [arXiv:1509.08127] [INSPIRE].
K.-T. Chen, Iterated path integrals, Bull. Am. Math. Soc. 83 (1977) 831 [INSPIRE].
F.C.S. Brown, Multiple zeta values and periods of moduli spaces \( {\mathfrak{M}}_{0,n} \), Annales Sci. Ecole Norm. Sup. 42 (2009) 371 [math.AG/0606419] [INSPIRE].
A.B. Goncharov, A simple construction of Grassmannian polylogarithms, arXiv:0908.2238 [INSPIRE].
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ArXiv ePrint: 1608.08116
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Lam, H.T., von Hippel, M. Resumming the POPE at one loop. J. High Energ. Phys. 2016, 11 (2016). https://doi.org/10.1007/JHEP12(2016)011
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DOI: https://doi.org/10.1007/JHEP12(2016)011