Integral Transformations for Conformally Invariant Celestial Amplitudes

TL;DR

The paper introduces an integral transformation for celestial gluon amplitudes that simplifies their structure and reveals invariance conditions under conformal transformations.

Contribution

It proposes a novel integral transformation inspired by string theory that maps celestial amplitudes to new variables, enabling analysis of conformal invariance.

Findings

Derived constraints on -, four-, and n-point amplitudes.

Constructed a consistent inverse transformation.

Showed invariance conditions are necessary for conformal symmetry.

Abstract

We propose an integral transformation for celestial gluon amplitudes that maps the celestial coordinates \((z_i,\bar z_i)\) to a new set of complex variables \((s_i,\bar s_i)\), 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 an overall normalization. Applying this transformation to celestial MHV amplitudes, we derive constraints on \((s_i,\bar s_i)\) for three-, four-, and general \(n\)-point amplitudes, and show that these conditions are necessary for invariance under global conformal transformations.