On Unitarity of Tree-Level String Amplitudes

Abstract

Four-particle tree-level scattering amplitudes in string theory are magically consistent with unitarity, reflected in the non-trivial fact that beneath the critical dimension, the residues of the amplitudes on massive poles can be expanded in partial waves with all positive coefficients. While this follows (rather indirectly) from the no-ghost theorem, the simplicity of the statement and its fundamental importance for the physical consistency of string theory begs for a more direct and elementary understanding. In this note we take a step in this direction by presenting a new expression for the partial wave coefficients of string amplitudes, given by surprisingly simple double/triple contour integrals for open/closed strings. This representation allows us to directly prove unitarity of all superstring theories in $D\le 6$ spacetime dimensions, and can also be used to determine various asymptotics of the partial waves at large mass levels.

arXiv comment37 pages

References in corpus (4)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• Asymptotic level density in heterotic string theory and rotating black holes
• Strings from Massive Higher Spins: The Asymptotic Uniqueness of the Veneziano Amplitude
• Positivity of the Veneziano Amplitude in $D=4$

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• Multiparticle Factorization and the Rigidity of String Theory
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• Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon
• Unitarity Cuts of the Worldsheet
• On the positivity of Coon amplitude in D=4
• Cutting the Coon Amplitude
• Positivity of the Veneziano Amplitude in $D=4$
• Celestial insights into the S-matrix bootstrap
• On the positivity of the hypergeometric Veneziano amplitude
• Multipositivity Bounds for Scattering Amplitudes
• Field theory expansions of string theory amplitudes
• Uniqueness Criteria for the Virasoro-Shapiro Amplitude
• Positivity of the Hypergeometric Coon Amplitude
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Lectures in Quantum Gravity
• On-shell Supersymmetry and higher-spin amplitudes
• Regge Limit of One-Loop String Amplitudes
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• Worldsheet for Generalized Veneziano Amplitudes