Revisiting the Conformally Soft Sector with Celestial Diamonds

TL;DR

This paper explores the structure of celestial diamonds in celestial CFT, linking conformally soft charges, memory effects, and dressings, and proposes a 2D effective description for the soft sector.

Contribution

It introduces a detailed framework connecting celestial diamonds with soft charges, dressings, and effective 2D descriptions in celestial CFT, advancing understanding of the soft sector.

Findings

Conformally soft charges are expressed via light ray integrals.

Top corners of Goldstone diamonds relate to conformal dressings.

Sub-leading soft dressings are computed for gauge theory and gravity.

Abstract

Celestial diamonds encode the structure of global conformal multiplets in 2D celestial CFT and offer a natural language for describing the conformally soft sector. The operators appearing at their left and right corners give rise to conformally soft factorization theorems, the bottom corners correspond to conserved charges, and the top corners to conformal dressings. We show that conformally soft charges can be expressed in terms of light ray integrals that select modes of the appropriate conformal weights. They reside at the bottom corners of memory diamonds, and ascend to generalized currents. We then identify the top corners of the associated Goldstone diamonds with conformal Faddeev-Kulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions. Finally, we combine these ingredients to speculate on 2D effective descriptions for the conformally soft sector of celestial CFT.