Conference

In this introductory talk, I will present a new perspective about quantum gravity which is rooted deeply in a renewed understanding of local symmetries in Gravity that appears when we decompose gravitational systems into subsystems. I will emphasize the central role of the corner symmetry group in capturing all the necessary data needed to glue back seamlessly quantum spacetime regions. I will present how the charge conservation associated with these symmetries encoded the dynamics of null surfaces. Finally, I will also present how the representation theory of the corner symmetry arises and provides a representation of quantum geometry, and I will show that deformations of this symmetry can be the explanation for a fundamental planckian cut-off. I will also mention how these symmetry groups reduce to asymptotic symmetry groups and control asymptotic gravitational dynamics when the entangling sphere is moved to infinity. If time permits, I will explain how these symmetries control asymptotic gravitational dynamics. And I will describe how they provide a new picture of the nature of quantum radiation. Overall, this new paradigm allows to connect semi-classical gravitational physics, S-matrix theory, and non-perturbative quantum gravity techniques. The talk's goal is to give an overall flavor of how these connections appear from an elementary understanding of symmetries.

Speaker Order: Ankit Aggarwal, University of Amsterdam Monireh Ahmadpour, University of Tehran Giovanni Canepa, Centre de Physique Théorique Roukaya Dekhil, Ludwig Maximilian University Arnaud Delfante, University of Mons Florian Ecker, Technische Universität Wien Gloria Odak, Centre de Physique Théorique

We begin by reviewing the role of coadjoint orbits in the representation theory of nilpotents groups and then, to connect with the recent applications in physics of coadjoint orbits "around the corner" of the mathematical framework developed by Kirillov, we review the classification of coadjoint orbits of the Virasoro group. This will allow us to connect with more recent developments, including e.g. the study of coadjoint orbits of BMS algebras.

This lecture aims at introducing the notion of asymptotic symmetries in gravity and the derivation of the related surface charges by means of covariant phase space techniques. First, after a short historical introduction, I will rigorously define what is meant by “asymptotic symmetry” within the so-called gauge-fixing approach. The problem of fixing consistent boundary conditions and the formulation of the variational principle will be briefly discussed. In the second part of the lecture, I will introduce the covariant phase space formalism, as conceived by Wald and coworkers thirty years ago, which adapts the Hamiltonian formulation of classical mechanics to Lagrangian covariant field theories. With the help of this fantastic tool, I will elaborate on the construction of canonical surface charges associated with asymptotic symmetries and address the crucial questions of their conservation and integrability on the phase space. In the third and last part, I will conclude with an analysis of the algebraic properties of the surface charges, describing in which sense they represent the asymptotic symmetry algebra in full generality, without assuming conservation or integrability. For pedagogical purposes, the theoretical concepts will be illustrated throughout in the crucial and well-known case of radiative asymptotically flat spacetimes in four dimensions, as described by Einstein’s theory of General Relativity, and where many spectacular and unexpected features appear even in the simplest case of historical asymptotically Minkowskian boundary conditions. In particular, I will show that the surface charge algebra contains the physical information on the flux of energy and angular momentum at null infinity in the presence of gravitational radiation.