Phenomenological consequences of the modern S-matrix Bootstrap programme

In this talk I will cover some of the recent successes of the S-matrix bootstrap. I will show how simple ideas of causality and unitarity lead to non-trivial bound on the space of EFTs. In particular we will see how to bound the EFT of long confining flux tubes, and the leading deviations in the SM EFT. The recurring theme on both examples will be that non-dispersive observables can be bounded using the S-matrix bootstrap toolkit.