Scaling exponents of Mellin amplitudes for deriving bounds on flat space S-matrices from bounds on chaos

TL;DR

This paper establishes a connection between the Regge growth bounds of flat space S-matrices and chaos bounds in conformal correlators via Mellin amplitude scaling exponents, providing a new method to derive S-matrix bounds from conformal field theory.

Contribution

It introduces a novel inequality between Mellin amplitude scaling exponents that links flat space S-matrix bounds to conformal correlator bounds using the AdS/CFT correspondence.

Findings

Derived the inequality A' ≥ A for Mellin amplitude exponents.

Established the Regge growth bound of flat space S-matrices from chaos bounds.

Showed A' = A under certain conditions with finite intermediate spins.

Abstract

We study an inequality between a scaling exponent $A$ in the Regge limit of tree-level flat space S-matrices with external massless scalars and another scaling exponent $A'$ in the Regge limit of the corresponding four-point scalar conformal correlators by using scaling exponents of Mellin amplitudes. We derive $A'\ge A$, which leads to the Regge growth bound of tree-level flat space S-matrices from the chaos bound in the flat space limit of the AdS/CFT correspondence, from polynomial boundedness of the Mellin amplitudes for local bulk descriptions. We also show $A'=A$ from the conformal block expansion in the $t$-channel with finite intermediate spins when coefficients are not small in the flat space limit.