Infrared and Holographic Aspects of the $S$-Matrix in Gauge Theory and Gravity

Abstract

Soft theorems in gauge theory and gravity encode the universal properties of scattering amplitudes as the zero frequency limit of one or more external states is approached. When the participating particles are treated in the massless limit, the soft theorems are known to depend only on the directions of the states on null infinity. Leveraging this fact, we develop dual two-dimensional descriptions of soft theorems, recasting them as Ward identities of such dual models on the celestial sphere. This is done by first postulating putative holographic representations of the hard scattering amplitudes and dressing the asymptotic operators with appropriate two-dimensional analogues of the Wilson line. The soft theorems are then recovered by inserting currents that generate the Ward identities of the dual models. In addition to providing naturally holographic representations of the soft theorems, we see that it becomes possible to develop presentations of the asymptotic symmetries associated to these theorems entirely in terms of the dual two-dimensional fields. In the course of carrying out this analysis for soft theorems at leading order and beyond, we find that the two-dimensional dual description of soft theorems may be directly inferred by drawing analogies with the existing framework of asymptotic symmetry charges. We find that the soft charges generating the asymptotic symmetries can be brought into correspondence with dual two-dimensional currents, while the two-dimensional Wilson loops can be related to the hard parts of the conserved charges. Consequently, we rewrite the triality of asymptotic symmetries, soft theorems and conserved charges directly in the language of a class of two-dimensional theories.

v1: 81 pages

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