# OPE inversion in Mellin space

## TL;DR

This paper explores an inversion formula in Mellin space for conformal field theory correlators, inspired by Caron-Huot's light-cone inversion, aiming to extract OPE data more efficiently.

## Contribution

It introduces a novel Mellin space inversion formula for OPE coefficients, extending the existing light-cone inversion approach to Mellin amplitude representations.

## Key findings

- Partial development of the Mellin space inversion formula
- Connections established between Mellin amplitudes and OPE data
- Potential for improved analysis of conformal correlators

## Abstract

The fundamental ingredients that build the observables in conformal field theory are the spectrum of operators and the OPE coefficients, or equivalently, the two- and three-point functions of the theory. Recently an inversion formula solving the OPE coefficients by a convolution over the light-cone double-discontinuities of the correlator has been found by Simon Caron-Huot. Taking into account that the same OPE data determine the Mellin amplitude representation of the correlator, motivate us to look for an analogous inversion formula in Mellin space, which we develops partially on this paper.