CFT Dispersion Relation For Mixed Correlators

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 re-summing the data obtained by the Lorentzian inversion formula.

Continuing the work of Dean Carmi and Simon Caron-Haut we generalize the kernel for unequal scaling dimensions and provide a numerical method to verify the dispersion relation.