At its core, Nature is described by gauge systems such as electrodynamics and gravitation. These theories are written in terms of redundant quantum fields in spacetime, where certain redefinitions of variables---technically called gauge transformations---affect no locally observable physical property. However, it was recently realized that some such redundancies are, in fact, genuine symmetries that do affect observables, akin to the translations or rotations of a mechanical system. The corresponding "large" gauge transformations are "asymptotic symmetries," a prominent example of which is the intriguing Bondi-Metzner-Sachs (BMS) group relevant for gravitational radiation. More generally, asymptotic symmetries provide an unexpected new window into the study of all gauge theories at low energies and large distances.
Classifying asymptotic symmetries and modelling their effects is therefore crucial for both conceptual and practical scientific reasons. Indeed, such symmetries are a key ingredient in the quantization of any gauge theory. While this was surprisingly overlooked for a long time even in the simple case of electrodynamics, it has even deeper consequences for gravitation, whose quantization has been eluding physicists for a century. One could thus imagine using asymptotic symmetries to compute the entropy of black holes or resolve the information paradox---ideas that have all been put forward in recent years. On the practical end, asymptotic symmetries have observable consequences for gauge theories in the infrared, either through their remnants in scattering amplitudes of particles, or through their effects in gravitational waves---which have finally become observable after a century of suspense.
With these motivations in mind, the purpose of this MSCA project was twofold. First, to understand the experimental signatures of asymptotic symmetries, such as gravitational memory effects or Berry phases. The latter are uncharted territory, and their scope goes well beyond high-energy physics, as analogous phases exist in shallow water dynamics. Second, to establish the structure of asymptotic symmetries (and their unitary representations) needed for the description of so-called "dressed states" in quantum field theory, which are crucial in particle colliders. This reformulation opens the door to numerous applications and to a conceptual leap in our understanding of both particles physics and quantum gravity.
