Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory

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.

arXiv comment25 pages, 4 figures

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• Distributions in CFT II. Minkowski Space
• Momentum space spinning correlators and higher spin equations in three dimensions
• A Scattering Amplitude in Conformal Field Theory
• Conformal partial waves in momentum space
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• Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions
• Recursive construction of the operator product expansion in curved space
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• $n$-point functions in Conformal Quantum Mechanics: A Momentum Space Odyssey
• Conformal bootstrap in momentum space at finite volume