On Unitarity of Bespoke Amplitudes

TL;DR

This paper investigates the unitarity constraints of bespoke four-point amplitudes, constructing generalized superstring amplitudes and analyzing their high-energy behavior to identify which satisfy unitarity and Regge sum rules.

Contribution

It introduces new bespoke amplitude constructions, applies partial wave unitarity constraints, and delineates conditions for their high-energy consistency and Regge behavior.

Findings

Bespoke superstring generalizations satisfy dual resonance.

Amplitudes with non-linear Regge trajectories are ruled out.

A subclass with zero mass gap is superpolynomially bounded.

Abstract

We use partial wave unitarity to constrain various bespoke four-point amplitudes. We start by constructing bespoke generalizations of the type I superstring amplitude, which we show satisfy dual resonance and have suitable high-energy limits. By analyzing the behavior of partial wave coefficients for highly massive states, we strictly rule out all bespoke amplitudes with asymptotically non-linear Regge trajectories and place constraints on the first few non-trivial parameters in asymptotically linear cases. Finally, we argue that while a large class of unitary bespoke amplitudes fails to satisfy Regge Sum Rules, there exists a smaller sub-class with a vanishing mass gap that is superpolynomially bounded.