Shadows and Soft Exchange in Celestial CFT

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.

43 pages, 1 figure

References in corpus (2)

• Infrared Divergences in QED, Revisited
• Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity

Cited by in corpus (11)

• Bridging Carrollian and Celestial Holography
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Soft Scalars and the Geometry of the Space of Celestial CFTs
• A Comment on Loop Corrections to the Celestial Stress Tensor
• Celestial Locality and the Jacobi Identity
• Revisiting the Shadow Stress Tensor in Celestial CFT
• Celestial IR divergences in general most-subleading-color gluon and gravity amplitudes
• AdS correction to the Faddeev-Kulish state: Migrating from the Flat Peninsula
• $p$-Forms on the Celestial Sphere
• Dynamical Edge Modes in Yang-Mills Theory
• Charge algebra for non-abelian large gauge symmetries at $O(r)$