I will explain how the S-matrix Bootstrap for massless particles can be used to constrain the space of Effective Field Theories (EFT). In particular, I will discuss the S-matrix bootstrap for massless particles in unitary, relativistic two dimensional quantum field theories. In the context of flux tube physics, this allows us to constrain several terms in the S-matrix low energy expansion or -- equivalently -- on Wilson coefficients of several irrelevant operators showing up in the flux tube effective action. The S-matrices living at the boundary of the allowed space exhibit an intricate pattern of resonances with one sharper resonance whose quantum numbers, mass and width are precisely those of the world-sheet axion previously proposed. Finally, I will present work in progress on pion scattering amplitudes and the chiral Lagrangian. The general method should be extendable to other massless S-matrices including gauge and gravity theories.