Lorentzian OPE Inversion Formula: A Geometric Perspective

TL;DR

This paper offers a geometric interpretation of the Lorentzian OPE inversion formula by relating it to Radon transforms and Mellin amplitudes, providing new insights into conformal field theory analysis.

Contribution

It introduces an auxiliary four-point function linked via Radon transform, connecting Mellin amplitudes to partial wave amplitudes through a geometric perspective.

Findings

Mellin amplitudes are equivalent to partial wave amplitudes.

The auxiliary function relates to traditional functions via Radon transform.

Provides a geometric interpretation of the inversion formula.

Abstract

We give a new perspective on the Lorentzian OPE inversion formula of arXiv:1703.00278, building on arXiv:2302.06469. We introduce an ``auxiliary'' fourpoint function that can be related to the traditionally defined ones via a Radon transform. The Mellin amplitudes associated with this auxiliary function can be shown to be equivalent to the conventional partial wave amplitudes. This has the intuitive geometrical meaning of a generalization of the Projection-Slice Theorem.