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Classification of Convergent OPE Channels for Lorentzian CFT Four-Point Functions

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arxiv 2005.09105 v6 pith:RRFFDEIW submitted 2020-05-18 hep-th

Jiaxin Qiao This is my paper · ORCID
classification hep-th
keywords functionslorentzianfour-pointconvergenceclassificationconfigurationsgiveproperties
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abstract

We analyze the convergence properties of operator product expansions (OPE) for Lorentzian CFT four-point functions of scalar operators. We give a complete classification of Lorentzian four-point configurations. All configurations in each class have the same OPE convergence properties in s-, t- and u-channels. We give tables including the information of OPE convergence for all classes. Our work justifies that in a subset of the configuration space, Lorentzian CFT four-point functions are genuine analytic functions. Our results are valid for unitary CFTs in $d\geq2$. Our work also provides some Lorentzian regions where one can do bootstrap analysis in the sense of functions.

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Cited by 4 Pith papers

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  1. Do null defects dream of conformal symmetry?

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    Null line defects preserve a large conformal algebra that constrains their correlators to shockwave-plane discontinuities, and a restricted test-function space resolves the ill-defined ultraboosted gauge potential.

  2. Effective dynamics of open 2D CFTs

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    The momentum-space thermal four-point response function of scalar primaries in an arbitrary 2D CFT is expressed as an infinite sum over global conformal blocks of Meijer G-functions.

  3. Lorentzian OPE Inversion Formula: A Geometric Perspective

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    The Mellin transform of a Radon-transformed (auxiliary) four-point function reproduces the Lorentzian OPE partial wave amplitudes, giving a geometric projection-slice interpretation.

  4. Correlation functions of von Neumann entropy

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    Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.

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