Abstract
General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions.
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ArXiv ePrint: 1912.05550
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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.
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Gillioz, M., Lu, X., Luty, M.A. et al. Convergent momentum-space OPE and bootstrap equations in conformal field theory. J. High Energ. Phys. 2020, 102 (2020). https://doi.org/10.1007/JHEP03(2020)102
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DOI: https://doi.org/10.1007/JHEP03(2020)102