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Soft theorems in gauge theory and gravity encode the universal properties ofscattering amplitudes as the zero frequency limit of one or more externalstates is approached. When the participating particles are treated in themassless limit, the soft theorems are known to depend only on the directions ofthe states on null infinity. Leveraging this fact, we develop dualtwo-dimensional descriptions of soft theorems, recasting them as Wardidentities of such dual models on the celestial sphere. This is done by firstpostulating putative holographic representations of the hard scatteringamplitudes and dressing the asymptotic operators with appropriatetwo-dimensional analogues of the Wilson line. The soft theorems are thenrecovered by inserting currents that generate the Ward identities of the dualmodels. In addition to providing naturally holographic representations of thesoft theorems, we see that it becomes possible to develop presentations of theasymptotic symmetries associated to these theorems entirely in terms of thedual two-dimensional fields. In the course of carrying out this analysis forsoft theorems at leading order and beyond, we find that the two-dimensionaldual description of soft theorems may be directly inferred by drawing analogieswith the existing framework of asymptotic symmetry charges. We find that thesoft charges generating the asymptotic symmetries can be brought intocorrespondence with dual two-dimensional currents, while the two-dimensionalWilson loops can be related to the hard parts of the conserved charges.Consequently, we rewrite the triality of asymptotic symmetries, soft theoremsand conserved charges directly in the language of a class of two-dimensionaltheories.

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