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arXiv · 2503.08774

Conformal dispersion relation for mixed correlators

Dean Carmi·Javier Moreno·Shimon Sukholuski
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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.

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Dean Carmi, Javier Moreno, Shimon Sukholuski. 2025-03-11. Conformal dispersion relation for mixed correlators. https://arxiv.org/abs/2503.08774

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