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

This work is based upon classical achievements of S-matrix bootstrap together with an outline of its modern applications. We establish the connection from integral scattering amplitudes to the use of bootstrap technique in modern conformal field theories and holography. Using bootstrap approach, we provide the calculations for integral representations for the sine-Gordon S-matrix elements. Minimal form factors of this model are related to recent studies of certain conformal field theories. We also propose the extension of the sine-Gordon bootstrap equations to the space of conformal correlators known as celestial amplitudes.