On the positivity of the hypergeometric Veneziano amplitude

Abstract

Recently, an infinite family of one-parameter generalisations of the Veneziano amplitude were bootstrapped using as input assumptions an integer mass spectrum, crossing symmetry, high-energy boundedness, and exchange of finite spins. This new result was dubbed the hypergeometric Veneziano amplitude, with a real-valued deformation parameter r. For concreteness we work in a setup where the lowest-mass state is a tachyon of mass $m_0^2=-1$ and using the partial-wave decomposition and the positivity of said decomposition's coefficients we are able to bound the deformation parameter to $r\ge 0$ and, also, to obtain an upper bound on the number of spacetime dimensions $D\le 26$, which is the critical dimension of bosonic string theory.

v1: 19 pages + 8 pages appendices, v2: reference added, v3: published version

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Cited by in corpus (3)

• Positivity of the Hypergeometric Coon Amplitude
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Worldsheet for Generalized Veneziano Amplitudes