QGI Seminar: William Donnelly "Gravitational edge modes and hydrodynamics"
Symmetries play an essential role in classical and quantum mechanics and can act as a bridge between a classical system and its quantization. One of the most famous examples is Wigner's classification of representations of the Poincaré group by mass and spin. In general relativity, one can identify a phase space associated to a three-dimensional region of space and an infinite-dimensional Lie group of symmetries acting at its two-dimensional boundary which is called the corner symmetry group. In this talk, William Donnelly (Perimeter Institute) gives a complete classification of positive area coadjoint orbits of the corner symmetry group when the boundary is a two-sphere, following the classification of positive mass representations of the Poincaré group. The latter reduces to the classification of orbits of the symmetry group of compressible hydrodynamics. This allows him to identify geometric invariants with their hydrodynamical counterparts - the total mass of the fluid corresponds to the total surface area, while the fluid vorticity corresponds to the outer curvature of the boundary surface. William also comments on the prospects for quantizing these orbits, and on potential implications for entanglement in quantum gravity.
Based on arxiv:2012.10367 with L. Freidel, A.J. Speranza, and S.F. Moosavian.
The Quantum Gravity and Information seminar series is a joint initiative between the Max Planck Institute for Gravitational Physics (Potsdam), the University of Amsterdam and University College London.
This talk was recorded on March 7, 2021.