Massless S-matrix bootstraps and RG flows

A bstract We find complete solutions of S -matrix bootstrap equations for the scatterings of massless particles in (1+1) dimensions with A n symmetries. We show that only three types (minimal, diagonal, and saturated cases) of these S -matrices can generate RG flows that lead to UV-complete theories, and other RG flows predicted in [11] are inconsistent with the bootstrap equations. Using these S -matrices, we derived the TBA equations and corresponding Y -systems that generate the RG flows between the IR and UV CFTs.