Abstract
Some quantities in quantum field theory are dominated by so-called leading logs and can be re-summed to all loop orders. In this work we introduce a notion of stampede which is a simple time-evolution of a bunch of particles which start their life in a corner — on the very right say — and hop their way to the opposite corner — on the left — through the repeated action of a quantum Hamiltonian. Such stampedes govern leading logs quantities in certain quantum field theories. The leading euclidean OPE limit of correlation functions in the fishnet theory and null double-scaling limits of correlators in \( \mathcal{N} \) = 4 SYM are notable examples. As an application, we use these results to extend the beautiful bootstrap program of Coronado [1] to all octagons functions with arbitrary diagonal bridge length.
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References
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].
G. Frobenius, Uber die charaktere der symmetrischer gruppe, Königliche Gesellschaft der Wissenschaften, Göttingen, Germany (1900), pp 516–534 [DOI].
Frame, Robinson and Thrall, The Hook Graphs of the Symmetric Group, Can. J. Math. 6 (1954) 316.
I. Gessel and G. Viennot, Binomial determinants, paths, and hook length formulae, Adv. Math. 58 (1985) 300.
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].
J. Caetano, O. Gürdoğan and V. Kazakov, Chiral limit of \( \mathcal{N} \) = 4 SYM and ABJM and integrable Feynman graphs, JHEP 03 (2018) 077 [arXiv:1612.05895] [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 [Addendum ibid. 117 (2016) 259903] [arXiv:1512.06704] [INSPIRE].
A.C. Aitken, The monomial expansion of determinantal symmetric functions, Proc. Math. Roy. Soc. Edinb. 61 (1943) 300.
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].
L.F. Alday and A. Bissi, Higher-spin correlators, JHEP 10 (2013) 202 [arXiv:1305.4604] [INSPIRE].
N. Beisert, The complete one loop dilatation operator of N = 4 superYang-Mills theory, Nucl. Phys. B 676 (2004) 3 [hep-th/0307015] [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].
P. Vieira and T. Wang, Tailoring Non-Compact Spin Chains, JHEP 10 (2014) 035 [arXiv:1311.6404] [INSPIRE].
A. Sever, P. Vieira and T. Wang, From Polygon Wilson Loops to Spin Chains and Back, JHEP 12 (2012) 065 [arXiv:1208.0841] [INSPIRE].
T. Bargheer, F. Coronado and P. Vieira, Octagons II: Strong Coupling, arXiv:1909.04077 [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].
A.V. Belitsky and G.P. Korchemsky, Exact null octagon, JHEP 05 (2020) 070 [arXiv:1907.13131] [INSPIRE].
C. Bercini, V. Gonçalves and P. Vieira, Light-Cone Bootstrap of Higher Point Functions and Wilson Loop Duality, Phys. Rev. Lett. 126 (2021) 121603 [arXiv:2008.10407] [INSPIRE].
C. Bercini, V. Gonçalves, A. Homrich and P. Vieira, The Wilson Loop — Large Spin OPE Dictionary, arXiv:2110.04364 [INSPIRE].
A.V. Belitsky and G.P. Korchemsky, Crossing bridges with strong Szegő limit theorem, JHEP 04 (2021) 257 [arXiv:2006.01831] [INSPIRE].
I. Kostov, V.B. Petkova and D. Serban, Determinant Formula for the Octagon Form Factor in \( \mathcal{N} \) = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett. 122 (2019) 231601 arXiv:1903.05038] [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].
S. Derkachov and E. Olivucci, Conformal quantum mechanics & the integrable spinning Fishnet, JHEP 11 (2021) 060 [arXiv:2103.01940] [INSPIRE].
E. Olivucci, Hexagonalization of Fishnet integrals. Part I. Mirror excitations, JHEP 11 (2021) 204 [arXiv:2107.13035] [INSPIRE].
D.J. Grabiner and P.M. Magyar, Random Walks in Weyl Chambers and the Decomposition of Tensor Powers, J. Algebr. Comb. 2 (1993) 239.
I.M. Gessel and D. Zeilberger, Random walk in a Weyl chamber, Proc. Am. Math. Soc. 115 (1992) 27.
A. Okounkov, Andrei and N. Reshetikhin, Correlation function of Schur process with application to local geometry of a random 3-dimensional Young diagram, J. Am. Math. Soc. 16 (2003) 581.
B. Lacroix-A-Chez-Toine, P.L. Doussal, S.N. Majumdar and G. Schehr, Non-interacting fermions in hard-edge potentials, J. Stat. Mech. 2018 (2018) 123103.
K. Johansson, Non-intersecting paths, random tilings and random matrices, Probab. Theor. Related Fields 123 (2002) 225.
J. Baik, Random vicious walks and random matrices, Commun. Pure Appl. Math. 53 (2000) 1385.
K. Johansson, From Gumbel to Tracy-Widom, Probab. Theory Relat. Fields 138 (2007) 75.
S. Caron-Huot and F. Coronado, Ten dimensional symmetry of \( \mathcal{N} \) = 4 SYM correlators, JHEP 03 (2022) 151 [arXiv:2106.03892] [INSPIRE].
A. Antunes, M.S. Costa, V. Goncalves and J.V. Boas, Lightcone bootstrap at higher points, JHEP 03 (2022) 139 [arXiv:2111.05453] [INSPIRE].
T. Fleury and V. Goncalves, Decagon at Two Loops, JHEP 07 (2020) 030 [arXiv:2004.10867] [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].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
F.A. Dolan and H. Osborn, Conformal partial wave expansions for N = 4 chiral four point functions, Annals Phys. 321 (2006) 581 [hep-th/0412335] [INSPIRE].
B. Eden and A. Sfondrini, Three-point functions in \( \mathcal{N} \) = 4 SYM: the hexagon proposal at three loops, JHEP 02 (2016) 165 [arXiv:1510.01242] [INSPIRE].
B. Basso, V. Goncalves and S. Komatsu, Structure constants at wrapping order, JHEP 05 (2017) 124 [arXiv:1702.02154] [INSPIRE].
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Olivucci, E., Vieira, P. Stampedes I: fishnet OPE and octagon Bootstrap with nonzero bridges. J. High Energ. Phys. 2022, 17 (2022). https://doi.org/10.1007/JHEP07(2022)017
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DOI: https://doi.org/10.1007/JHEP07(2022)017