A spacetime derivation of the Lorentzian OPE inversion formula

David Simmons-Duffin, Douglas Stanford, Edward Witten

Research output: Contribution to journalArticlepeer-review

159 Scopus citations


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.

Original languageEnglish (US)
Article number85
JournalJournal of High Energy Physics
Issue number7
StatePublished - Jul 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • Conformal Field Theory
  • Conformal and W Symmetry


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