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.
Highlights
Something interesting about quantum gravity in the bulk
We identify the top corners of the associated Goldstone diamonds with conformal FaddeevKulish dressings and compute the sub-leading conformally soft dressings in gauge theory and gravity which are important for finding nontrivial central extensions
The Kac-Moody symmetry associated to the leading soft theorem in gauge theory has been shown to arise from a Chern-Simons theory [5]
Summary
Let us start with the definition of conformal primary wavefunctions. These are functions of a bulk point X ∈ R1,3 and a boundary point (w, w) ∈ C on the celestial sphere. Mellin transformed plane waves with s > 0 are obtained by multiplying (2.5) with w and w These are only gauge equivalent to conformal primaries (2.1). Celestial amplitudes are obtained from ordinary amplitudes by Mellin transforming the energy of each external particle They obey universal factorization theorems, called conformally soft theorems, when one of the conformal dimensions is taken to special values of ∆ ∈ Z (for integer bulk spin). The symplectic partners of the ∆ = 1 Goldstone modes in (2.12) and (2.13) were constructed in [2] via a special limiting procedure to produce non-trivial memory effects They are given by the ∆ = 1 conformally soft photon and graviton wavefunctions. The CS wavefunctions with φCS ≡ Θ(X2)φ1 describe solutions that are glued across the lightcone (and will reappear in section 4) while the CS wavefunctions with φCS ≡ log(X2)δ(q · X) correspond to shockwave solutions [3]
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