Shadows and Soft Exchange in Celestial CFT

TL;DR

This paper explores soft exchange phenomena in celestial conformal field theories across various dimensions, revealing how symmetry principles govern infrared divergences and soft theorems in gauge and gravitational theories.

Contribution

It introduces a model capturing soft exchange and infrared effects in celestial CFT, demonstrating the role of Goldstone modes and shadow transforms in these processes.

Findings

Reproduces abelian infrared divergences in 2D.

Captures infrared-finite soft exchange in higher dimensions.

Derives leading soft theorems using symmetry considerations.

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.