Abstract
In this work, we compute one-loop planar five-point functions in \( \mathcal{N}=4 \) super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross-ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.
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References
N. Beisert et al., Review of AdS/CFT Integrability: An Overview, Lett. Math. Phys. 99 (2012) 3 [arXiv:1012.3982] [INSPIRE].
N. Gromov, V. Kazakov, S. Leurent and D. Volin, Quantum Spectral Curve for Planar \( \mathcal{N}=4 \) super-Yang-Mills Theory, Phys. Rev. Lett. 112 (2014) 011602 [arXiv:1305.1939] [INSPIRE].
N. Gromov, Introduction to the Spectrum of N = 4 SYM and the Quantum Spectral Curve, arXiv:1708.03648 [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in \( \mathcal{N}=4 \) SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of Correlation Functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure Constants and Integrable Bootstrap in Planar N = 4 SYM Theory,arXiv:1505.06745[INSPIRE].
B. Basso, F. Coronado, S. Komatsu, H.T. Lam, P. Vieira and D.-l. Zhong, Asymptotic Four Point Functions, arXiv:1701.04462 [INSPIRE].
N. Drukker and J. Plefka, The structure of n-point functions of chiral primary operators in N = 4 super Yang-Mills at one-loop, JHEP 04 (2009) 001 [arXiv:0812.3341] [INSPIRE].
T. Bargheer, J. Caetano, T. Fleury, S. Komatsu and P. Vieira, Handling Handles I: Nonplanar Integrability, arXiv:1711.05326 [INSPIRE].
T Bargheer, J. Caetano, T. Fleury, S. Komatsu and P. Vieira, Handling Handles II: Stratification and Data Analysis, to appear.
B. Eden, Y. Jiang, D. le Plat and A. Sfondrini, Colour-dressed hexagon tessellations for correlation functions and non-planar corrections, arXiv:1710.10212 [INSPIRE].
B. Eden, P.S. Howe, C. Schubert, E. Sokatchev and P.C. West, Extremal correlators in four-dimensional SCFT, Phys. Lett. B 472 (2000) 323 [hep-th/9910150] [INSPIRE].
J. Erdmenger and M. Pérez-Victoria, Nonrenormalization of next-to-extremal correlators in N = 4 SYM and the AdS/CFT correspondence, Phys. Rev. D 62 (2000) 045008 [hep-th/9912250] [INSPIRE].
B.U. Eden, P.S. Howe, E. Sokatchev and P.C. West, Extremal and next-to-extremal n point correlators in four-dimensional SCFT, Phys. Lett. B 494 (2000) 141 [hep-th/0004102] [INSPIRE].
D. Chicherin, J. Drummond, P. Heslop and E. Sokatchev, All three-loop four-point correlators of half-BPS operators in planar \( \mathcal{N}=4 \) SYM, JHEP 08 (2016) 053 [arXiv:1512.02926] [INSPIRE].
B. Basso and L.J. Dixon, Gluing Ladder Feynman Diagrams into Fishnets, Phys. Rev. Lett. 119 (2017) 071601 [arXiv:1705.03545] [INSPIRE].
O. Gürdoğan and V. Kazakov, New Integrable 4D Quantum Field Theories from Strongly Deformed Planar \( \mathcal{N}=4 \) Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 117 (2016) 201602 [arXiv:1512.06704] [INSPIRE].
C. Sieg and M. Wilhelm, On a CFT limit of planar γ i -deformed \( \mathcal{N}=4 \) SYM theory, Phys. Lett. B 756 (2016) 118 [arXiv:1602.05817] [INSPIRE].
J. Caetano, O. Gürdoğan and V. Kazakov, Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs, arXiv:1612.05895 [INSPIRE].
D. Chicherin, V. Kazakov, F. Loebbert, D. Müller and D.-l. Zhong, Yangian Symmetry for Bi-Scalar Loop Amplitudes, arXiv:1704.01967 [INSPIRE].
N. Gromov, V. Kazakov, G. Korchemsky, S. Negro and G. Sizov, Integrability of Conformal Fishnet Theory, JHEP 01 (2018) 095 [arXiv:1706.04167] [INSPIRE].
D. Chicherin, V. Kazakov, F. Loebbert, D. Müller and D.-l. Zhong, Yangian Symmetry for Fishnet Feynman Graphs, Phys. Rev. D 96 (2017) 121901 [arXiv:1708.00007] [INSPIRE].
G. Arutyunov, M. de Leeuw and A. Torrielli, The Bound State S-matrix for AdS 5 × S 5 Superstring, Nucl. Phys. B 819 (2009) 319 [arXiv:0902.0183] [INSPIRE].
G. Arutyunov and S. Frolov, The S-matrix of String Bound States, Nucl. Phys. B 804 (2008) 90 [arXiv:0803.4323] [INSPIRE].
Z. Bajnok and R.A. Janik, Four-loop perturbative Konishi from strings and finite size effects for multiparticle states, Nucl. Phys. B 807 (2009) 625 [arXiv:0807.0399] [INSPIRE].
Z. Bajnok, R.A. Janik and T. Lukowski, Four loop twist two, BFKL, wrapping and strings, Nucl. Phys. B 816 (2009) 376 [arXiv:0811.4448] [INSPIRE].
T. Lukowski, A. Rej and V.N. Velizhanin, Five-Loop Anomalous Dimension of Twist-Two Operators, Nucl. Phys. B 831 (2010) 105 [arXiv:0912.1624] [INSPIRE].
N. Beisert, The SU(2|2) dynamic S-matrix, Adv. Theor. Math. Phys. 12 (2008) 945 [hep-th/0511082] [INSPIRE].
N. Beisert, The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry, J. Stat. Mech. 0701 (2007) P01017 [nlin/0610017].
G. Arutyunov, S. Frolov and M. Zamaklar, The Zamolodchikov-Faddeev algebra for AdS 5 × S 5 superstring, JHEP 04 (2007) 002 [hep-th/0612229] [INSPIRE].
G. Arutyunov and S. Frolov, Foundations of the AdS 5 × S 5 Superstring. Part I, J. Phys. A 42 (2009) 254003 [arXiv:0901.4937] [INSPIRE].
N. Beisert, The S-matrix of AdS/CFT and Yangian symmetry, PoS(SOLVAY)002 [arXiv:0704.0400] [INSPIRE].
M. de Leeuw, Bound States, Yangian Symmetry and Classical r-matrix for the AdS 5 × S 5 Superstring, JHEP 06 (2008) 085 [arXiv:0804.1047] [INSPIRE].
F. Loebbert, Lectures on Yangian Symmetry, J. Phys. A 49 (2016) 323002 [arXiv:1606.02947] [INSPIRE].
M. de Leeuw, The Bethe Ansatz for AdS 5 × S 5 Bound States, JHEP 01 (2009) 005 [arXiv:0809.0783] [INSPIRE].
N. Beisert and F. Spill, The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure, Commun. Math. Phys. 285 (2009) 537 [arXiv:0708.1762] [INSPIRE].
A. Torrielli, Classical r-matrix of the SU(2|2) SYM spin-chain, Phys. Rev. D 75 (2007) 105020 [hep-th/0701281] [INSPIRE].
J. Caetano and T. Fleury, Fermionic Correlators from Integrability, JHEP 09 (2016) 010 [arXiv:1607.02542] [INSPIRE].
H.-Y. Chen, N. Dorey and K. Okamura, On the scattering of magnon boundstates, JHEP 11 (2006) 035 [hep-th/0608047] [INSPIRE].
R. Roiban, Magnon Bound-state Scattering in Gauge and String Theory, JHEP 04 (2007) 048 [hep-th/0608049] [INSPIRE].
G. Arutyunov and S. Frolov, The Dressing Factor and Crossing Equations, J. Phys. A 42 (2009) 425401 [arXiv:0904.4575] [INSPIRE].
Z. Bajnok, A. Hegedus, R.A. Janik and T. Lukowski, Five loop Konishi from AdS/CFT, Nucl. Phys. B 827 (2010) 426 [arXiv:0906.4062] [INSPIRE].
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 III. The two-particle contributions, JHEP 08 (2014) 085 [arXiv:1402.3307] [INSPIRE].
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ArXiv ePrint: 1711.05327
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Fleury, T., Komatsu, S. Hexagonalization of correlation functions II: two-particle contributions. J. High Energ. Phys. 2018, 177 (2018). https://doi.org/10.1007/JHEP02(2018)177
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DOI: https://doi.org/10.1007/JHEP02(2018)177