Abstract
We consider four-point correlation functions of protected single-trace scalar operators in planar \( \mathcal{N} \) = 4 supersymmetric Yang-Mills (SYM). We conjecture that all loop corrections derive from an integrand which enjoys a ten-dimensional symmetry. This symmetry combines spacetime and R-charge transformations. By considering a 10D light-like limit, we extend the correlator/amplitude duality by equating large R-charge octagons with Coulomb branch scattering amplitudes. Using results from integrability, this predicts new finite amplitudes as well as some Feynman integrals.
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B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Hidden symmetry of four-point correlation functions and amplitudes in N = 4 SYM, Nucl. Phys. B 862 (2012) 193 [arXiv:1108.3557] [INSPIRE].
B. Eden, P. Heslop, G.P. Korchemsky and E. Sokatchev, Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N = 4 SYM, Nucl. Phys. B 862 (2012) 450 [arXiv:1201.5329] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps, JHEP 11 (2016) 125 [arXiv:1609.00007] [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].
D. Chicherin, A. Georgoudis, V. Gonçalves and R. Pereira, All five-loop planar four-point functions of half-BPS operators in \( \mathcal{N} \) = 4 SYM, JHEP 11 (2018) 069 [arXiv:1809.00551] [INSPIRE].
F. Coronado, Perturbative four-point functions in planar \( \mathcal{N} \) = 4 SYM from hexagonalization, JHEP 01 (2019) 056 [arXiv:1811.00467] [INSPIRE].
F. Coronado, Bootstrapping the Simplest Correlator in Planar \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory to All Loops, Phys. Rev. Lett. 124 (2020) 171601 [arXiv:1811.03282] [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, Determinant Formula for the Octagon Form Factor in N=4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 122 (2019) 231601 [arXiv:1903.05038] [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, The Octagon as a Determinant, JHEP 11 (2019) 178 [arXiv:1905.11467] [INSPIRE].
K.A. Intriligator, Bonus symmetries of N = 4 superYang-Mills correlation functions via AdS duality, Nucl. Phys. B 551 (1999) 575 [hep-th/9811047] [INSPIRE].
B. Eden, A.C. Petkou, C. Schubert and E. Sokatchev, Partial nonrenormalization of the stress tensor four point function in N = 4 SYM and AdS/CFT, Nucl. Phys. B 607 (2001) 191 [hep-th/0009106] [INSPIRE].
J.L. Bourjaily, A. DiRe, A. Shaikh, M. Spradlin and A. Volovich, The Soft-Collinear Bootstrap: N = 4 Yang-Mills Amplitudes at Six and Seven Loops, JHEP 03 (2012) 032 [arXiv:1112.6432] [INSPIRE].
J.L. Bourjaily, P. Heslop and V.-V. Tran, Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 116 (2016) 191602 [arXiv:1512.07912] [INSPIRE].
S. Lee, S. Minwalla, M. Rangamani and N. Seiberg, Three point functions of chiral operators in D = 4, N = 4 SYM at large N, Adv. Theor. Math. Phys. 2 (1998) 697 [hep-th/9806074] [INSPIRE].
F. Aprile, J. Drummond, P. Heslop and H. Paul, Double-trace spectrum of N = 4 supersymmetric Yang-Mills theory at strong coupling, Phys. Rev. D 98 (2018) 126008 [arXiv:1802.06889] [INSPIRE].
F. Aprile et al., Single particle operators and their correlators in free \( \mathcal{N} \) = 4 SYM, JHEP 11 (2020) 072 [arXiv:2007.09395] [INSPIRE].
S. Caron-Huot and A.-K. Trinh, All tree-level correlators in AdS5 × S5 supergravity: hidden ten-dimensional conformal symmetry, JHEP 01 (2019) 196 [arXiv:1809.09173] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of Correlation Functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
B. Basso, F. Coronado, S. Komatsu, H.T. Lam, P. Vieira and D.-l. Zhong, Asymptotic Four Point Functions, JHEP 07 (2019) 082 [arXiv:1701.04462] [INSPIRE].
L.F. Alday, B. Eden, G.P. Korchemsky, J. Maldacena and E. Sokatchev, From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].
L.F. Alday and J.M. Maldacena, Gluon scattering amplitudes at strong coupling, JHEP 06 (2007) 064 [arXiv:0705.0303] [INSPIRE].
N. Berkovits and J. Maldacena, Fermionic T-duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection, JHEP 09 (2008) 062 [arXiv:0807.3196] [INSPIRE].
N. Beisert, R. Ricci, A.A. Tseytlin and M. Wolf, Dual Superconformal Symmetry from AdS5 × S5 Superstring Integrability, Phys. Rev. D 78 (2008) 126004 [arXiv:0807.3228] [INSPIRE].
Z. Bern et al., The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 78 (2008) 045007 [arXiv:0803.1465] [INSPIRE].
J.M. Drummond, J. Henn, G.P. Korchemsky and E. Sokatchev, Hexagon Wilson loop = six-gluon MHV amplitude, Nucl. Phys. B 815 (2009) 142 [arXiv:0803.1466] [INSPIRE].
L.J. Mason and D. Skinner, The Complete Planar S-matrix of N = 4 SYM as a Wilson Loop in Twistor Space, JHEP 12 (2010) 018 [arXiv:1009.2225] [INSPIRE].
S. Caron-Huot, Notes on the scattering amplitude/Wilson loop duality, JHEP 07 (2011) 058 [arXiv:1010.1167] [INSPIRE].
B. Eden, G.P. Korchemsky and E. Sokatchev, From correlation functions to scattering amplitudes, JHEP 12 (2011) 002 [arXiv:1007.3246] [INSPIRE].
L.F. Alday, J.M. Henn, J. Plefka and T. Schuster, Scattering into the fifth dimension of N = 4 super Yang-Mills, JHEP 01 (2010) 077 [arXiv:0908.0684] [INSPIRE].
S. Caron-Huot and D. O’Connell, Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions, JHEP 08 (2011) 014 [arXiv:1010.5487] [INSPIRE].
Z. Bern, J.S. Rozowsky and B. Yan, Two loop four gluon amplitudes in N = 4 superYang-Mills, Phys. Lett. B 401 (1997) 273 [hep-ph/9702424] [INSPIRE].
J.M. Drummond, J. Henn, V.A. Smirnov and E. Sokatchev, Magic identities for conformal four-point integrals, JHEP 01 (2007) 064 [hep-th/0607160] [INSPIRE].
B. Eden, G.P. Korchemsky and E. Sokatchev, More on the duality correlators/amplitudes, Phys. Lett. B 709 (2012) 247 [arXiv:1009.2488] [INSPIRE].
Z. Bern, L.J. Dixon and V.A. Smirnov, Iteration of planar amplitudes in maximally supersymmetric Yang-Mills theory at three loops and beyond, Phys. Rev. D 72 (2005) 085001 [hep-th/0505205] [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Exact null octagon, JHEP 05 (2020) 070 [arXiv:1907.13131] [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons I: Combinatorics and Non-Planar Resummations, JHEP 08 (2019) 162 [arXiv:1904.00965] [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons II: Strong Coupling, arXiv:1909.04077 [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Octagon at finite coupling, JHEP 07 (2020) 219 [arXiv:2003.01121] [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Crossing bridges with strong Szegő limit theorem, JHEP 04 (2021) 257 [arXiv:2006.01831] [INSPIRE].
A.V. Belitsky, Null octagon from Deift-Zhou steepest descent, arXiv:2012.10446 [INSPIRE].
I. Kostov and V.B. Petkova, Octagon with finite BRIDGE: free fermions and determinant identities, JHEP 06 (2021) 098 [arXiv:2102.05000] [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in \( \mathcal{N} \) = 4 SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure Constants and Integrable Bootstrap in Planar N = 4 SYM Theory, arXiv:1505.06745 [INSPIRE].
Y. Jiang, S. Komatsu, I. Kostov and D. Serban, Clustering and the Three-Point Function, J. Phys. A 49 (2016) 454003 [arXiv:1604.03575] [INSPIRE].
B. Basso and D.-L. Zhong, Three-point functions at strong coupling in the BMN limit, JHEP 04 (2020) 076 [arXiv:1907.01534] [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of Correlation Functions II: Two-Particle Contributions, JHEP 02 (2018) 177 [arXiv:1711.05327] [INSPIRE].
M. De Leeuw, B. Eden, D. Le Plat, T. Meier and A. Sfondrini, Multi-particle finite-volume effects for hexagon tessellations, JHEP 09 (2020) 039 [arXiv:1912.12231] [INSPIRE].
T. Fleury and V. Goncalves, Decagon at Two Loops, JHEP 07 (2020) 030 [arXiv:2004.10867] [INSPIRE].
N.I. Usyukina and A.I. Davydychev, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett. B 305 (1993) 136 [INSPIRE].
B. Basso and L.J. Dixon, Gluing Ladder Feynman Diagrams into Fishnets, Phys. Rev. Lett. 119 (2017) 071601 [arXiv:1705.03545] [INSPIRE].
B. Basso, L.J. Dixon, D.A. Kosower, A. Krajenbrink and D.-l. Zhong, Fishnet four-point integrals: integrable representations and thermodynamic limits, JHEP 07 (2021) 168 [arXiv:2105.10514] [INSPIRE].
Z. Bern, M. Czakon, L.J. Dixon, D.A. Kosower and V.A. Smirnov, The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory, Phys. Rev. D 75 (2007) 085010 [hep-th/0610248] [INSPIRE].
B. Eden and V.A. Smirnov, Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations, JHEP 10 (2016) 115 [arXiv:1607.06427] [INSPIRE].
S. Derkachov and E. Olivucci, Exactly solvable magnet of conformal spins in four dimensions, Phys. Rev. Lett. 125 (2020) 031603 [arXiv:1912.07588] [INSPIRE].
S. Derkachov and E. Olivucci, Exactly solvable single-trace four point correlators in χCFT4, JHEP 02 (2021) 146 [arXiv:2007.15049] [INSPIRE].
B. Basso, L.J. Dixon and G. Papathanasiou, Origin of the Six-Gluon Amplitude in Planar N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 124 (2020) 161603 [arXiv:2001.05460] [INSPIRE].
D.N. Blaschke, H. Steinacker and M. Wohlgenannt, Heat kernel expansion and induced action for the matrix model Dirac operator, JHEP 03 (2011) 002 [arXiv:1012.4344] [INSPIRE].
F. Aprile, J.M. Drummond, H. Paul and M. Santagata, The Virasoro-Shapiro amplitude in AdS5 × S5 and level splitting of 10d conformal symmetry, JHEP 11 (2021) 109 [arXiv:2012.12092] [INSPIRE].
T. Abl, P. Heslop and A.E. Lipstein, Towards the Virasoro-Shapiro amplitude in AdS5 × S5, JHEP 04 (2021) 237 [arXiv:2012.12091] [INSPIRE].
J. Drummond, C. Duhr, B. Eden, P. Heslop, J. Pennington and V.A. Smirnov, Leading singularities and off-shell conformal integrals, JHEP 08 (2013) 133 [arXiv:1303.6909] [INSPIRE].
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Caron-Huot, S., Coronado, F. Ten dimensional symmetry of \( \mathcal{N} \) = 4 SYM correlators. J. High Energ. Phys. 2022, 151 (2022). https://doi.org/10.1007/JHEP03(2022)151
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DOI: https://doi.org/10.1007/JHEP03(2022)151