Positivity of the Veneziano Amplitude in Ten Dimensions

Abstract: The Veneziano amplitude describing the tree-level scattering of four open superstrings is expected to be consistent with unitarity in ten spacetime dimensions. While this follows indirectly from the no-ghost theorem, a direct proof at the level of the amplitude has only been found for $D\leq 6$. In this note, we close this gap by providing a complete proof for the partial-wave positivity of the Veneziano amplitude in $D\leq 10$, derived directly from its definition in terms of the Euler beta function. We also demonstrate that this proof can be modified to show positivity of a wider family of amplitudes relevant to the $S$-matrix bootstrap.