Uplift of Veneziano‑like deformations to fully consistent S‑matrices

Determine whether previously proposed four‑point deformations of the open‑string Veneziano amplitude can be embedded into a fully consistent, unitary, and causal S‑matrix with well‑defined m→n scattering amplitudes at all multiplicities.

Background

The paper reviews that many four‑point deformations of the Veneziano amplitude have been constructed in the literature. However, having a consistent four‑point amplitude does not guarantee that it extends to a full S‑matrix satisfying unitarity and causality for all processes.

By contrast, the present work provides a family of amplitudes arising from scattering on the Coulomb branch of planar N=4 SYM, which is argued to define a consistent tree‑level open‑string S‑matrix across couplings. The broader question of the consistency of other deformations remains unresolved.