In this M1 internship, the intern will revisit a problem as old as string theory itself: the quantum mechanical consistency of interactions between fundamental strings. More precisely, the intern will study the quantum mechanical scattering amplitude at the first order in perturbation theory. It is famously given by the Veneziano formula, derived in the 60s. While it has been known since the 70s that String Theory is consistent quantum mechanically, it has never been shown directly that the Veneziano formula respects a unitary evolution. Recently, it has been observed empirically that the Veneziano formula obeys a remarkable property, stronger than unitarity [1]. The intern will work on a mathematical proof of this property. In practice, this will amount to literally looking at the properties of the poles of the Euler beta function. As surprising as it may sound, more than 2 centuries after Euler, there are still simple things to understand about this object which can in addition tell us something new about string theory. [1] Eckner, Figueroa, Tourkine 2024, https://arxiv.org/abs/2401.08736