A Conformal Dispersion Relation: Correlations from Absorption
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.
Keywords
Cite
@article{arxiv.1910.12123,
title = {A Conformal Dispersion Relation: Correlations from Absorption},
author = {Dean Carmi and Simon Caron-Huot},
journal= {arXiv preprint arXiv:1910.12123},
year = {2020}
}
Comments
minor corrections, 35+6 pages, 7 figures