The S-matrix Bootstrap: From the Sine-Gordon Model to Celestial Amplitudes

We address the scattering problem in two-dimensional integrable models, focusing on the sine-Gordon theory. We use the S-matrix bootstrap approach based on analytical properties of the S-matrix to compute scattering amplitudes of the sine-Gordon model. We obtain original integral representations for the sine-Gordon scattering amplitudes involving bound states. Calculation of minimal form factors in this model follows directly from integral representations of scattering amplitudes. We also propose the extension of the sine-Gordon bootstrap equations to the space of conformal correlators known as celestial amplitudes.