Echoes of infrared universality: Soft theorems and asymptotic symmetries beyond the leading order.

Over the past decade, asymptotic symmetries of gauge and gravity theories have been shown to underlie universal features of scattering amplitudes in the infrared regime. In particular, soft theorems can be reinterpreted as Ward identities of asymptotic symmetries. This thesis explores these connections from two complementary perspectives: the scattering amplitude approach, where soft theorems directly constrain the $S$-matrix, and the general relativistic approach, where they appear as diffeomorphisms preserving the asymptotic fall-offs of the metric. In the first part, we extend the standard tree-level picture by incorporating loop corrections to soft theorems in quantum electrodynamics and gravity. We show that logarithmic terms in the photon and graviton soft expansions, absent at tree level, naturally arise from infrared effects and long-range interactions, and we interpret these corrections in terms of modified Ward identities for asymptotic symmetry charges. A detailed analysis reveals how the gravitational dressing of charged and massive states generates the additional loop-level structures observed in the subleading soft factors. In the second part, we shift focus to the celestial representation and the full soft tower at tree level. Working in the Newman–Penrose formalism, we study the Einstein–Maxwell system and derive recursion relations for an infinite family of asymptotic charges directly from the equations of motion. We identify suitable quasi-conserved charges that, when smeared over the celestial sphere, close into the celestial $sw_{1+\infty}$ algebra—a symmetry structure unifying the gravitational $w_{1+\infty}$ and electromagnetic $s$-algebras. We further discuss the extension to Einstein–Yang–Mills theory and the interplay between gauge and gravitational couplings. Taken together, these results provide new insights into the infrared structure of scattering amplitudes, the algebra of asymptotic symmetries, and their realization in theories with coupled gauge and gravitational interactions.