Abstract
At leading order, the $S$-matrices in QED and gravity are known to factorize, providing unambiguous determinations of the parts divergent due to infrared contributions. The soft $S$-matrices defined in this fashion are shown to be defined entirely in terms of two-dimensional models on the celestial sphere, involving two real scalar fields, allowing us to express the soft $S$-matrices for real as well as virtual divergences as two-dimensional correlation functions. We discuss what this means for finding holographic representations of scattering amplitudes in QED and gravity and comment on simple double copy structures that arise during the analysis.
Highlights
The concerns with divergences in the S-matrix for quantum field theories of interest revolved around complications deep in the ultraviolet
It has been known for a long time that S-matrices for theories having massless particles exhibit singularities not just in the UV, and in the infrared domain, where interacting particles approach arbitrarily low frequencies
While we provide a brief review of this we state at this point that according to factorization theorems, the soft divergences in QED and gravity can be collected into universal expressions which form a part of any scattering amplitude in these theories, and can be factored out, so to speak
Summary
The concerns with divergences in the S-matrix for quantum field theories of interest revolved around complications deep in the ultraviolet. It tells us that the analytic structure of the S-matrix in the infrared—something that appears to be dependent on the nature of interactions in the bulk—depends on data that is present entirely on the boundary of four-dimensional spacetime, namely null infinity in the form on BMS charges It suggests the possibility of realizing the entire S-matrix, at least in fundamentally massless theories like. While we provide a brief review of this, we state at this point that according to factorization theorems, the soft divergences in QED and gravity can be collected into universal expressions which form a part of any scattering amplitude in these theories, and can be factored out, so to speak In carrying out this factorization, we obtain an unambiguous definition of the soft S-matrix, and can ask whether these objects admit representations in terms of dynamical fields defined on the boundary.
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