Light transformation: A Celestial and Carrollian perspective

TL;DR

This paper investigates the role of light transformations in Celestial and Carrollian conformal field theories, revealing how symmetries fix operator product expansions and establish connections between different CFT branches.

Contribution

It demonstrates that Poincaré symmetries determine the leading singularity in Celestial CFT OPEs using light transforms, and explores the mapping between Carrollian CFT branches via light transformation.

Findings

Poincaré symmetries fix the leading OPE singularity in Celestial CFTs.

Light transforms relate different branches of Carrollian CFTs in 3D.

Consistency of symmetry-fixed OPEs with three-point function limits.

Abstract

In this paper, we first study the consequence of spacetime translations and Lorentz transformations on Celestial CFT OPEs. Working with the light transforms of the operators belonging to the modified Mellin basis, we found that the leading order singularity in the OPE of such operators could be fixed purely using Poincar\'e symmetries owing to the non-trivial action of the translations on these operators. The OPE coefficient is then fixed using the soft limit of the correlation functions. We check that this singular structure obtained from symmetries is consistent with the OPE limit of three-point functions. This approach could potentially be useful for studying Celestial CFT without adverting to bulk physics. As another goal, we explore the significance of light transformation in Carrollian CFTs. In the special cases we considered, we show that light transformation equips us with a map between two branches of Carroll CFT in $d=3$ dimension at the level of correlation functions in the near coincident limit.