Positivity of the hypergeometric Veneziano amplitude

Recently, an infinite family of one-parameter generalizations 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 m₀²=-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≥0 and, also, to obtain an upper bound on the number of spacetime dimensions D≤26, which is the critical dimension of bosonic string theory.