The High Energy Behavior of Mellin Amplitudes

TL;DR

This paper establishes high-energy bounds on Mellin amplitudes in conformal field theories, analogous to scattering amplitude bounds in quantum field theories, by analyzing their singularity structure.

Contribution

It proves bounds on Mellin amplitudes in CFTs under certain assumptions and conjectures a stronger bound supported by explicit examples.

Findings

Bounds are valid under specific technical conditions.

A stronger conjectured bound is supported by multiple examples.

The approach links singularity structure to amplitude bounds.

Abstract

In any consistent massive quantum field theory there are well known bounds on scattering amplitudes at high energies. In conformal field theory there is no scattering amplitude, but the Mellin amplitude is a well defined object analogous to the scattering amplitude. We prove bounds at high energies on Mellin amplitudes in conformal field theories, valid under certain technical assumptions. Such bounds are derived by demanding the absence of spurious singularities in position space correlators. We also conjecture a stronger bound, based on evidence from several explicit examples.