Open string amplitudes: singularities, asymptotics and new representations

Journal Article · Thu Apr 03 00:00:00 EDT 2025 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep04(2025)039· OSTI ID:2561313

Arkani-Hamed, Nima ^[1]; Figueiredo, Carolina ^[2]; Remmen, Grant N. ^[3]

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1. Institute for Advanced Study, Princeton, NJ (United States)
2. Princeton University, NJ (United States)
3. New York University, NY (United States)

Open string amplitudes at tree level have been studied for over fifty years. However, 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 finding explicit expressions for the factorization of amplitudes at general massive levels, which are seen to be determined by products of lower-point massless amplitudes with shifted kinematics. 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 derive new recursion relations for the amplitude, which when repeatedly applied reduce to infinite series representations with a wider domain of convergence than the usual integral representations. For the five-point case, we present a new closed-form expression for the amplitude that for the first time gives its analytic continuation to all of kinematic space. We also discuss novel relations between amplitudes at different kinematic points following from the recently observed “split” factorizations.

• Research Organization: Institute for Advanced Study, Princeton, NJ (United States)
• Sponsoring Organization: FCT/Portugal; USDOE Office of Science (SC)
• Grant/Contract Number: SC0009988
• OSTI ID: 2561313
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 4 Vol. 2025; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Bosonic Strings
Scattering Amplitudes
Superstrings and Heterotic Strings