Dual model amplitudes are meromorphic amplitudes involving the exchange of infinitely-many higher spin states. They are the staple of tree-level string theory, with the Veneziano and Virasoro-Shapiro amplitudes being their most famous representatives and also describe gauge theories in the large N limit.  

Amplitudes of this class must satisfy very constraining consistency conditions, which makes them good candidates for bootstrap approaches. Yet, only recently they are receiving the attention of the S-matrix bootstrap community, partly because many standard S-matrix bootstrap techniques are not well suited for their study.

In this talk I will show some recent progress in the analysis of dual model amplitudes from a bootstrap perspective using techniques from Regge theory of complex angular momentum. After a short motivation/introduction to dual model amplitudes and presenting the main ideas of Regge theory, I will explain how these techniques can be used to study them and showcase some recent results: the proof that dual model amplitudes require infinitely many trajectories to be consistent, and a numerical method to build consistent dual amplitudes with customizable spectrum and high energy behavior.