Open String Amplitudes: Singularities, Asymptotics, and New Representations

TL;DR

This paper explores open string amplitudes using a new binary geometry approach, providing explicit factorization, asymptotic analysis, recursion relations, and a novel five-point amplitude expression with full kinematic coverage.

Contribution

It introduces a systematic study of open string amplitudes via $u$ variables, including explicit factorization, asymptotics, recursion relations, and a new five-point amplitude formula.

Findings

Explicit factorization at massive levels

Asymptotic regimes with exponential and power-law behavior

New recursion relations and a closed-form five-point amplitude

Abstract

Open string amplitudes at tree level have been studied for over fifty years, but there is no known analytic form for general $n$-point amplitudes, and their conventional representation in terms of worldsheet integrals does not make many of their most basic physical properties manifest. Recently, a formulation of these amplitudes exposing the underlying "binary geometry" via the use of "$u$" variables has given us many insights into their basic features. In this paper, we initiate a systematic exploration of fundamental aspects of open string amplitudes from this new point of view. We begin by giving explicit expressions for the factorization of amplitudes at general massive levels. We then study the asymptotic behavior when subsets of kinematic variables become large, delineating regimes with exponential (generalized hard scattering) and power-law (generalized Regge) behavior. We also give precise expressions for the asymptotics, which reveal another example of the recently observed property of factorization away from poles. We finally derive new recursion relations and infinite series representations for the amplitude, and for five points, we present a new closed-form expression for the amplitude that for the first time gives its analytic continuation to all of kinematic space.