Shadows and Soft Exchange in Celestial CFT
Daniel Kapec, Prahar Mitra
TL;DR
Kapec and Mitra show that soft exchange in $(d+2)$-dimensional gauge and gravitational theories can be captured by a $d$-dimensional boundary theory within the celestial CFT framework. By leveraging asymptotic symmetries and their Goldstone edge modes, they derive a symmetry-determined soft action whose shadow transform yields a local $d$-dimensional dynamics that reproduce bulk infrared effects, including leading soft theorems across dimensions. The work unifies Abelian IR divergences, outlines magnetic and non-Abelian extensions, and introduces a boundary $BF$-type construction for gravity’s supertranslations, suggesting a holographic interpretation of celestial correlators. The results provide a principled, symmetry-based route to computing soft exchange and illuminate the role of shadow operators as the natural local degrees of freedom on the celestial sphere.
Abstract
We study exponentiated soft exchange in $d+2$ dimensional gauge and gravitational theories using the celestial CFT formalism. These models exhibit spontaneously broken asymptotic symmetries generated by gauge transformations with non-compact support, and the effective dynamics of the associated Goldstone "edge" mode is expected to be $d$-dimensional. The introduction of an infrared regulator also explicitly breaks these symmetries so the edge mode in the regulated theory is really a $d$-dimensional pseudo-Goldstone boson. Symmetry considerations determine the leading terms in the effective action, whose coefficients are controlled by the infrared cutoff. Computations in this model reproduce the abelian infrared divergences in $d=2$, and capture the re-summed (infrared finite) soft exchange in higher dimensions. The model also reproduces the leading soft theorems in gauge and gravitational theories in all dimensions. Interestingly, we find that it is the shadow transform of the Goldstone mode that has local $d$-dimensional dynamics: the effective action expressed in terms of the Goldstone mode is non-local for $d>2$. We also introduce and discuss new magnetic soft theorems. Our analysis demonstrates that symmetry principles suffice to calculate soft exchange in gauge theory and gravity.