Physics

In 1965, Lévy-Leblond introduced the ultra-relativistic cousin of the Poincaré symmetry and named it the Carrollian symmetry after Lewis Carroll (the pseudonym of the author of Alice’s adventures in Wonderland and Through the Looking-Glass). It can be seen as the counterpart of the non relativistic Galilean symmetry. Since then, Carrollian symmetry has become an active research topic in various fields, ranging from field theories, hydrodynamics, and more recently, gravity and black holes. In this talk, I will give an introductory review of the Carrollian symmetry and Carrollian physics, especially focusing on the emergence of Carrollian hydrodynamics in gravity and black holes

Over the past decade, many infrared phenomena of gauge theories, such as soft theorems and memory effects, have been shown to be manifestations of asymptotic symmetries which persist to the spacetime boundary. In this talk, I will discuss ongoing work, in collaboration with Robert Myers and Ana-Maria Raclariu, which recasts the asymptotic symmetries of gauge theories in Minkowski spacetime through conformal mappings. Through a mapping to the Einstein static universe, I will describe how conservation of asymptotic charge can be viewed as a smoothness constraint for image sources passing through spacelike infinity. Additionally, I will sketch how asymptotic charge flux through a subregion of null infinity is mapped to edge modes. This will then allow us to quantify fluctuations in asymptotic charge flux by relation to edge mode entropies, which have been well-studied in literature. Altogether, the general theme of my talk will be how new insights can be obtained by conformally mapping asymptotic structures of gauge theories to various settings.

The detection of gravitational waves has opened up new observational windows into the physics of black holes and has the potential to shed light on how imposing unitary evolution modifies the near horizon dynamics. In this talk, I will present how recent developments in holography have provided a way of understanding the physics of black hole thermalization in terms of the spacing statistics of black hole microstates. Based on this, I will suggest that the issue of measuring the quantum aspects of black holes from their ringdown depends on the spectral statistics of their microstates. I will then suggest that certain microstate statistics lend to the possibility of deviations in the ringdown behaviour of black holes in the form of “echoes” which might be interpreted as being due to Planck-scale microstructure near the horizon.

I will discuss work-in-progress for defining a new proposal for the covariant holographic entanglement entropy. The proposal instructs us to find maximal spacelike codimension-2 surfaces on timelike hypersurfaces in the bulk, followed by a minimization among all possible hypersurfaces in the right homology class. We describe and prove various properties of such minimax surfaces, and argue for their equivalence with the more familiar HRT and maximin proposals. Finally, we give compelling reasons to be interested in yet another entanglement entropy proposal: minimax surfaces allow us to prove all higher entropy cone inequalities, showing that the RT and HRT holographic entropy cones are indeed equivalent.

Many non-trivial ideas have been proposed to resolve singularities in quantum gravity. In this talk I argue that singularity resolution can be trivial in gravitational path integrals, because geodesically incomplete singular spacetimes are usually not included in the sum. For theories where this holds, there is no need to develop non-trivial ideas on singularity resolution. Instead, efforts should better be directed to understand tunneling processes and complex-valued spacetimes.

The semi-classical limit of spin foams leads to the Area Regge action. It was long thought that this action leads to flatness and does, in particular, not allow for propagating gravitons. I will present the first systematic studies of the continuum limit of the Area Regge action, using different versions of regular hypercubic lattices. These studies have shown that the Area Regge action does in its continuum limit, lead to leading order to general relativity, and thus to propagating gravitons. The higher order corrections depend on the choice of triangulation for the hypercubic lattice. However, there seems to be a preferred choice, for which the Area Regge action is not singular. In this case the correction term approximates the square of the Weyl curvature tensor, and can be interpreted to arise from an area metric dynamics. We therefore conjecture that the continuum limit of spin foams is described by an area metric theory.

The interplay between strong electronic interaction and non-trivial topology in magic-angle twisted bilayer graphene (tBLG) yields many intriguing phenomena that range from superconductivity to a spontaneous quantum anomalous Hall state with Chern number ±1. WIth the equilibrium phase diagram under much scrutiny, a better theoretical understanding of the excitation spectrum of tBLG is crucial to reveal experimental signatures of competing phases and discern possible pathways of controlling their behavior out of equilibrium. To this end, we study an effective Wannier-orbital model from Kang and Vafek (2019) in the strong coupling limit, which captures the Chern state at three quarters filling as well as its competition with proximal stripe charge order. We compute the density and chiral excitation spectra as well as the charge gap as a function of the overlap of neighboring Wannier orbitals. Our results provide an experimental signature to detect the transition from the stripe phase to the Chern phase and offer insight into steering of the quantum anomalous Hall state via low-frequency driving.

Monitored quantum circuits, composed of local unitary operators and projective measurements, have recently emerged as a rich setting for studying non-equilibrium quantum dynamics. In such systems, sufficient densities of measurements can protect a highly-monitored steady state phase with area law entanglement. Furthermore, it has been shown that such area law phases can host a measurement-protected Ising ferromagnetic order. However, it is not yet known whether such measurement-protected order is a generic phenomenon or whether it relies on the discrete Ising symmetry. To begin answering this question, we introduce a circuit model with continuous symmetry where ferromagnetic order arises in the steady state. Notably, our model requires feedback based on measurement results in order to generate this ferromagnetic order

Black hole echoes have been considered as new probes to standard gravitational waveforms. Here, I consider reflections of scalar waves around a black hole as a model of black hole echoes arising from scalar fields. This problem is difficult due to the need for a proper understanding of the characteristic fields that propagate in numerical relativity. Using the "Einstein-Christoffel" system, I model the characteristic fields and the boundary conditions in such a way as to properly reflect scalar waves at a boundary using the full power of Einstein’s equations.