Properties of infinite product amplitudes: Veneziano, Virasoro, and Coon

Abstract

We detail the properties of the Veneziano, Virasoro, and Coon amplitudes. These tree-level four-point scattering amplitudes may be written as infinite products with an infinite sequence of simple poles. Our approach for the Coon amplitude uses the mathematical theory of $q$-analysis. We interpret the Coon amplitude as a $q$-deformation of the Veneziano amplitude for all $q\ge 0$ and discover a new transcendental structure in its low-energy expansion. We show that there is no analogous $q$-deformation of the Virasoro amplitude.

v1, 23 pages; v2, fixed minor typos

References in corpus (11)

• The EFT-Hedron
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Carving out the Space of Open-String S-matrix
• On Unitarity of Tree-Level String Amplitudes
• Four loop reciprocity of twist two operators in N=4 SYM
• On the unitarity and low energy expansion of the Coon amplitude
• Accumulation-Point Amplitudes in String Theory
• UV-Complete Gravity Amplitudes and the Triple Product
• Positivity of the Veneziano Amplitude in $D=4$
• Integrating three-loop modular graph functions and transcendentality of string amplitudes
• Confronting Dual Models of the Strong Interaction

Cited by in corpus (16)

• Cornering Large-$N_c$ QCD with Positivity Bounds
• Veneziano Variations: How Unique are String Amplitudes?
• Generalized Veneziano and Virasoro amplitudes
• Shedding black hole light on the emergent string conjecture
• The Stringy S-matrix Bootstrap: Maximal Spin and Superpolynomial Softness
• Cutting the Coon Amplitude
• On (Scalar QED) Gravitational Positivity Bounds
• On the positivity of the hypergeometric Veneziano amplitude
• Uniqueness Criteria for the Virasoro-Shapiro Amplitude
• Positivity of the Hypergeometric Coon Amplitude
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Lectures in Quantum Gravity
• Strings from Almost Nothing
• Worldsheet for Generalized Veneziano Amplitudes
• A glimpse into the Ultrametric spectrum