Abstract
We consider the so-called simplest correlation function of four infinitely heavy half-BPS operators in planar \( \mathcal{N} \) = 4 SYM in the limit when the operators are light-like separated in a sequential manner. We find a closed-form expression for the correlation function in this limit as a function of the ’t Hooft coupling and residual cross ratios. Our analysis heavily relies on the factorization of the correlation function into the product of null octagons and on the recently established determinant representation for the latter. We show that the null octagon is given by a Fredholm determinant of a certain integral operator which has a striking similarity to those previously encountered in the study of two-point correlation functions in exactly solvable models at finite temperature and of level spacing distributions in random matrices. This allows us to compute the null octagon exactly by employing a method of differential equations.
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References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
B. Basso, S. Komatsu and P. Vieira, Structure constants and integrable bootstrap in planar N = 4 SYM theory, arXiv:1505.06745 [INSPIRE].
T. Fleury and S. Komatsu, Hexagonalization of correlation functions, JHEP 01 (2017) 130 [arXiv:1611.05577] [INSPIRE].
B. Eden and A. Sfondrini, Tessellating cushions: four-point functions in \( \mathcal{N} \) = 4 SYM, JHEP 10 (2017) 098 [arXiv:1611.05436] [INSPIRE].
Z. Bajnok and R.A. Janik, From the octagon to the SFT vertex — Gluing and multiple wrapping, JHEP 06 (2017) 058 [arXiv:1704.03633] [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 SYM at all loops, Phys. Rev. Lett. 124 (2020) 171601 [arXiv:1811.03282] [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].
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].
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].
L.F. Alday et al., From correlation functions to Wilson loops, JHEP 09 (2011) 123 [arXiv:1007.3243] [INSPIRE].
L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].
G.P. Korchemsky, Energy correlations in the end-point region, JHEP 01 (2020) 008 [arXiv:1905.01444] [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Octagon at finite coupling, arXiv:2003.01121 [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons II: strong coupling, arXiv:1909.04077 [INSPIRE].
A.R. Its et al., Differential equations for quantum correlation functions, Int. J. Mod. Phys. B 4 (1990) 1003.
V.E. Korepin, N.M. Bogoliubov and A.G. Izergin, Quantum inverse scattering method and correlation functions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge U.K. (1993).
M.L. Mehta, Random matrices, 3rd edition, Elsevier Academic Press, London U.K. (2004).
C.A. Tracy and H. Widom, Level spacing distributions and the Bessel kernel, Commun. Math. Phys. 161 (1994) 289 [hep-th/9304063] [INSPIRE].
P. Forrester, Log-gases and random matrices, London Mathematical Society Monographs volume 34, Oxford University Press, Oxford U.K. (2010).
J. Harnad, Random matrices, random processes and integrable systems, Springer, Germany (2011).
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ArXiv ePrint: 1907.13131
Unité Mixte de Recherche 3681 du CNRS
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Belitsky, A., Korchemsky, G. Exact null octagon. J. High Energ. Phys. 2020, 70 (2020). https://doi.org/10.1007/JHEP05(2020)070
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DOI: https://doi.org/10.1007/JHEP05(2020)070