Multipositivity Bounds for Scattering Amplitudes

TL;DR

This paper derives an infinite set of multipositivity bounds that constrain higher-point scattering amplitudes, extending previous four-point focused constraints and impacting string theory and effective field theories.

Contribution

It introduces a novel framework of multipositivity bounds applicable to all tree-level higher-point amplitudes under minimal assumptions.

Findings

Rules out certain deformations of string amplitudes.

Imposes mixed-multiplicity bounds on Wilson coefficients.

Identifies that open string amplitudes saturate these bounds.

Abstract

Lorentz invariance, unitarity, and causality enforce powerful constraints on the theory space of physical scattering amplitudes. However, virtually all efforts in this direction have centered on the very simplest case of four-point scattering. In this work, we derive an infinite web of "multipositivity bounds" that nonlinearly constrain all tree-level higher-point scattering amplitudes under similarly minimal assumptions. Our construction rules out several deformations of the string and implies mixed-multiplicity bounds on the Wilson coefficients of planar effective field theories. Curiously, an infinite class of multipositivity bounds is exactly saturated by the amplitudes of the open string.