  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.
