Abstract
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 language | English |
---|---|
Article number | 9 |
Journal | Journal of High Energy Physics |
Volume | 2020 |
Issue number | 9 |
DOIs | |
State | Published - 1 Sep 2020 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2020, The Author(s).
Keywords
- Conformal Field Theory
- Field Theories in Higher Dimensions
ASJC Scopus subject areas
- Nuclear and High Energy Physics