A conformal dispersion relation: correlations from absorption

Dean Carmi, Simon Caron-Huot

Research output: Contribution to journalArticlepeer-review


We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its “absorptive part”, defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the “inverted” conformal block with the ordinary conformal block.

Original languageEnglish
Article number9
JournalJournal of High Energy Physics
Issue number9
StatePublished - 1 Sep 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).


  • Conformal Field Theory
  • Field Theories in Higher Dimensions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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