Lorentzian OPE inversion formula: A geometric perspective

Abstract

We give a new perspective on the Lorentzian operator product expansion inversion formula [S. Caron-Huot, Analyticity in spin in conformal theories, .; D. Simmons-Duffin, D. Stanford, and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, .], building on [P. Agarwal , companion paper, Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions, .]. 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. Published by the American Physical Society 2025