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A spacetime derivation of the Lorentzian OPE inversion formula

  • David Simmons-Duffin
  • Douglas Stanford
  • Edward Witten
Open Access
Regular Article - Theoretical Physics

Abstract

Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The derivation is simple in two dimensions but more involved in higher dimensions. We also derive a Lorentzian inversion formula in one dimension that sheds light on previous observations about the chaos regime in the SYK model.

Keywords

Conformal and W Symmetry Conformal Field Theory 

Notes

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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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • David Simmons-Duffin
    • 1
    • 2
  • Douglas Stanford
    • 2
  • Edward Witten
    • 2
  1. 1.Walter Burke Institute for Theoretical PhysicsCaltechPasadenaU.S.A.
  2. 2.Institute for Advanced StudyPrincetonU.S.A.

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