Revisiting the Conformally Soft Sector with Celestial Diamonds

TL;DR

The paper develops an intrinsic 2D description of the conformally soft sector in celestial CFT by organizing conformally soft theorems into celestial diamonds (memory and Goldstone variants). It provides explicit light-ray extrapolate-like constructions that map bulk bulk states to celestial primaries with definite Δ,J, and identifies soft charges as bottom-corner descendants while conformal dressings live at the top corners. It derives concrete expressions for leading and sub-leading soft operators in gauge theory and gravity, and shows how Goldstone and memory structures generate holomorphic currents and potential central extensions. By constructing conformally soft dressings (including sub-leading extensions) and proposing 2D effective models, the work lays groundwork for intrinsic 2D descriptions of the conformally soft sector and its role in infrared structure and memory effects in celestial CFTs.

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.

Figures (2)

• Figure 1: Celestial diamonds for the conformally soft (a) photons and (b) gravitons.
• Figure 2: The $\mathcal{O}_{\Delta,J}^\pm(w,{\bar{w}})$ correspond to light ray integrals of operator insertions at $\mathcal{I}^\pm$. For fixed $(w,{\bar{w}})$ this is illustrated by the antipodally placed blue (past) and red (future) contours.