On unitarity of the hypergeometric amplitude

A bstract The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with S -matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the ( r, m 2 , D ) parameter space as non-unitary, and establish another large subset of the ( r, m 2 , D ) parameter space where all of the residue’s partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.