On the positivity of the hypergeometric Veneziano amplitude

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 $m^2_0=-1$ and using the partial-wave decomposition and the positivity of said decomposition's coefficients we are able to bound the deformation parameter to $r \geq 0$ and, also, to obtain an upper bound on the number of spacetime dimensions $D \leq 26$, which is the critical dimension of bosonic string theory.