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Asymptotic Symmetries: from Concepts to Observations

Periodic Reporting for period 1 - SymCO (Asymptotic Symmetries: from Concepts to Observations)

Reporting period: 2020-09-01 to 2022-08-31

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.
This grant began in the Autumn of 2020 and ended in the Summer of 2023. All the work was carried out by the fellow, Blagoje Oblak, with the mentorship of the supervisor, Marios Petropoulos. Over the course of that period, ten papers were published under MSCA funding; two more are due to appear in the coming months, and will be mentioned here as well.

The results obtained during the above period fit in three categories: a prediction of new, potentially observable, gravitational memory effects (3 papers); conceptual studies of asymptotic symmetries (3 papers that have already appeared, 2 more to appear soon); and a spin-off of the project that has to do with applications to quantum Hall systems in condensed matter physics (4 papers).

1. Gyroscopic memory effects:
This work has led to three papers so far. Their gist is to study the effect of gravitational waves on a spinning gyroscope in spacetime. As we show in our papers, gravitational waves cause the gyroscope to precess in a distinctive, observable manner. Furthermore, our third paper describes the analogous effect of electromagnetic waves on magnetic dipoles. These results have been presented in numerous talks and conferences over several years.

2. Conceptual aspects of asymptotic symmetries:
These questions were studied in 3 published papers with rather different contents, and will also give rise to 2 more papers soon. Those already published are (i) a single-authored work on the relation between the motion of fluid parcels and time-dependent diffeomorphisms; (ii) a work on asymptotic symmetries in low-dimensional gravity, with a surprising algebraic structure that has crucial implications for thermodynamics; (iii) a paper on the higher-spin version of asymptotic symmetries, their Carrollian structure, and their surprising relevance for the simplest of all field theories---a free massless scalar. As for the 2 papers that now remain to appear, (i) the first is concerned with field-dependent central extensions of asymptotic symmetres in low-dimensional gravitation coupled to electrodynamics, and (ii) the second describes an asymptotic symmetry group whose irreducible unitary representations are dressed states in the sense of Kulish-Faddeev. Again, these results were presented in numerous talks and workshops.

3. Boundary degrees of freedom in quantum Hall systems:
Considerations on condensed matter physics have now led to 4 papers, all focussed on the study of boundary degrees of freedom on quantum Hall edges, where asymptotic symmetries akin to those of low-dimensional gravity play a key role. In particular, we were able to describe the effect of such symmetry transformations in terms of observable changes in the properties of electronic droplets in the plane.
The aforementioned projects go well beyond the state of the art. As above, I will split them in three categories:

1. Gyroscopic memory effects:
These were never before even considered in the literature, and they have the added virtue that the precession rate coincides with a crucial "dual mass aspect" that was only known, till now, for purely mathematical reasons. The very idea to study gyroscopes in gravitational waves is highly original, and we were lucky to find an exceptionally pretty result, with potential applications for next-generation gravitational-wave detectors.

2. Conceptual aspects of asymptotic symmetries:
Following the sequence of five papers mentioned above, the novelty of studying fluid motion from a group-theoretic perspective is a crucial advance in hydrodynamics per se. As regards the two other papers on asymptotic symmetries, they also make leaps in new territories involving exotic asymptotic symmetries, Carrollian structures, and higher-spin generalizations. Their impact so far has been to reframe the discussion of flat-space holography in both low and high spacetime dimensions. Finally, the 2 upcoming papers are crucial: the one on field-dependent central extensions provides a fresh perspective on radiative ambiguities, while that on dressed states as representations of an extended asymptotic symmetry group is a revolutionary new proposal that has eluded the community for a decade.

3. Boundary degrees of freedom in quantum Hall systems:
The use of asymptotic-symmetry-inspired tools to study condensed matter systems was essentially never heard of until we developed our approach. In particular, our paper on anisotropic droplets exhibits the rich and surprising effects of such symmetry transformations on realistic samples, with both conceptual and practical implications for condensed matter physics as a whole.
The orientation of a gyroscope (in red) is changed by the passage of a burst of gravitational waves.