Integral transformations for conformally invariant celestial amplitudes

We propose an integral transformation for celestial amplitudes for massless particles that maps the celestial coordinates ( z i , z ¯ i ) to a new set of complex variables ( s i , s ¯ i ) , inspired by the structure of closed string scattering amplitudes. A consistent inverse transformation is constructed by regulating a divergence associated with translational redundancy and absorbing it into a normalization factor. Applying this transformation to celestial MHV amplitudes, we derive constraints on ( s i , s ¯ i ) for three-, four-, and general n -point amplitudes, and show that these conditions are necessary for invariance under global conformal transformations. The physical data of the external particles are encoded in the new variables ( s j , s ¯ j ) .