Bespoke Dual Resonance

Abstract

Dual resonance is one of the great miracles of string theory. At a fundamental level, it implies that the particles exchanged in different channels are subtly equivalent. Furthermore, it is inextricably linked to the property of exceptionally tame high-energy behavior. In this paper, we present explicit, closed-form expressions for a new class of dual resonant amplitudes describing an infinite tower of spins for an arbitrary mass spectrum. In particular, the input of our construction is a user-defined, fully customizable choice of masses. The resulting "bespoke" amplitudes are well behaved in the ultraviolet and analytic except at simple poles whose residues are polynomial in the momentum transfer, in accordance with locality. The absence of branch cuts can be seen using Newton's identities, but can also be made manifest by expressing the amplitudes as a simple dlog integral of the Veneziano amplitude that remaps the linear Regge trajectories of the string to a tunable spectrum. We identify open regions of parameter space that firmly deviate from string theory but nevertheless comport with partial wave unitarity. Last but not least, we generalize our construction to the scattering of any number of particles in terms of a dlog transform of the Koba-Nielsen worldsheet integral formula.

arXiv comment36 pages, 3 figures

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Cited by in corpus (18)

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• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• Multiparticle Factorization and the Rigidity of String Theory
• Bootstrap Principle for the Spectrum and Scattering of Strings
• Open String Amplitudes: Singularities, Asymptotics, and New Representations
• 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
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Consistent actions for massive particles interacting with electromagnetism and gravity
• Lectures in Quantum Gravity
• On the number of Regge trajectories for dual amplitudes
• Strings from Almost Nothing
• Worldsheet for Generalized Veneziano Amplitudes
• String Theory from Maximal Supersymmetry
• Higher-Spin and Higher-Point Constraints on Stringy Amplitudes