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.
Highlights
Gauge theories and gravitational theories in asymptotically flat spacetimes exhibit well-known universal infrared behavior
Soft theorems govern the form of scattering amplitudes at the boundaries of kinematic space, and repeated soft exchange exponentiates in a way that is independent of the microscopic details of the scattering process
We demonstrate that the shadow transform of the Goldstone mode has local d-dimensional dynamics, and that those dynamics fully reproduce the effects of soft exchange
Summary
Gauge theories and gravitational theories in asymptotically flat spacetimes exhibit well-known universal infrared behavior. Conservation, but the local transformations are more akin to Goldstone bosons for an infinite-dimensional symmetry group These universal features find natural expressions in the celestial conformal field theory (CFT) formalism. The introduction of the infrared regulator breaks these symmetries, so the effective action can contain symmetry breaking terms that give an action to the Goldstone modes and Ssoft1⁄2φs is the leading symmetry breaking term It takes the form of a (nonlocal) mass term for the flat connection Ca in the case of Abelian gauge theory.
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