Conformal dispersion relation for mixed correlators
Abstract
Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and conformal correlators. We derive a position-space dispersion relation for scalar four-point mixed correlation functions in an arbitrary conformal field theory. This formula expresses the correlator in terms of its integrated double discontinuity times a kinematic kernel. The kernel is analytically computed, and expressed in a remarkably simple form as a two-variable Appell function. The dispersion kernel is found by solving a coupled partial differential equation that the kernel obeys. Numerical checks of the dispersion relation are successfully performed for generalized free field correlators. Finally, we show that our position-space dispersion relation is equivalent to a Cauchy-type dispersion relation of the Mellin amplitude of the correlator.
Cite
@article{arxiv.2503.08774,
title = {Conformal dispersion relation for mixed correlators},
author = {Dean Carmi and Javier Moreno and Shimon Sukholuski},
journal= {arXiv preprint arXiv:2503.08774},
year = {2025}
}
Comments
11 pages. Version 2: typos corrected; discussion and references updated. Published in Phys. Rev. D Lett