22038 2305.08914 10.1007/JHEP10(2023)153 153 153 The five-point bootstrap Regular Article - Theoretical Physics 1 23 2023 10 25 2023 7 17 2023 10 6 2023 10 25 The Author(s) 2023 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2023 2023 10 10 David Poland david.poland@yale.edu Valentina Prilepina valentina.prilepina.1@ulaval.ca Petar Tadić petar.tadic@yale.edu https://ror.org/03v76x132 grid.47100.32 0000 0004 1936 8710 Department of Physics Yale University New Haven CT 06520 USA https://ror.org/013m0ej23 grid.420198.6 0000 0000 8658 0851 Perimeter Institute for Theoretical Physics Waterloo ON N2L 2Y5 Canada Abstract We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation. Keywords Correlation Functions Scale and Conformal Symmetries Conformal and W Symmetry ArXiv ePrint: 2305.08914