Welcome & Opening Remarks

• Luca Ciambelli (Perimeter Institute)
• Celine Zwikel (Perimeter Institute)

Room: PI/1-100 - Theatre

Review Talk: A primer on the covariant phase space formalism

• Adrien Fiorucci (Technische Universität Wien)

Room: PI/1-100 - Theatre 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.

Review Talk: A primer on the covariant phase space formalism cont.

• Adrien Fiorucci (Technische Universität Wien)

Room: PI/1-100 - Theatre

Review Talk: An introduction to coadjoint orbits

• Andrea Campoleoni (University Of Mons)

Room: PI/1-100 - Theatre 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.

Review Talk: An introduction to coadjoint orbits cont.

• Andrea Campoleoni (University Of Mons)

Room: PI/1-100 - Theatre

Gong Show

• Gloria Odak (Centre de Physique Théorique)
• Giovanni Canepa (Centre de Physique Théorique)
• Monireh Ahmadpour (University of Tehran)
• Florian Ecker (Technische Universität Wien)
• Roukaya Dekhil (Ludwig Maximilian University of Munich)
• Arnaud Delfante (University of Mons)
• Ankit Aggarwal (University of Amsterdam)

Room: PI/1-100 - Theatre 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

Local Holography and corner symmetry: A paradigm for quantum gravity

• Laurent Freidel (Perimeter Institute)

Room: PI/1-100 - Theatre 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.

Residual gauge symmetries in the front form

• Sucheta Majumdar (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre The goal of this talk is to discuss residual gauge symmetries in electromagnetism and gravity in Dirac's front form. Working in the light-cone gauge, I will demonstrate how the large gauge transformations and BMS supertranslations may be obtained from residual gauge invariance of the Hamiltonian action. The residual gauge symmetries in this (2+2) formulation share some striking similarities with the asymptotic symmetries in the conventional (3+1) Hamiltonian formulation. I will illustrate this fact using the example of electromagnetism and show how the the zero modes play a crucial role akin to boundary degrees of freedom in the asymptotic analysis at spatial infinity à la Henneaux-Troessaert.

Carrollian Perspective on Celestial Holography

• Romain Ruzziconi (Technische Universität Wien)

Room: PI/1-100 - Theatre The flat space holography program aims at describing quantum gravity in asymptotically flat spacetime in terms of a dual lower-dimensional field theory. Two different roads to construct flat space holography have emerged. The first consists of a 4d bulk / 3d boundary duality, called Carrollian holography, where 4d gravity is suggested to be dual to a 3d Carrollian CFT living on the null boundary of the spacetime. The second is a 4d bulk / 2d boundary duality, called celestial holography, where 4d gravity is dual to a 2d CFT living on the celestial sphere. I will argue that these two seemingly contradictory proposals are actually related. The Carrollian operators will be mapped to the celestial operators using an appropriate integral transform. The Ward identities of the sourced Carrollian CFT, encoding the gravitational flux-balance laws, will be shown to reproduce those of the 2d celestial CFT, encoding the bulk soft theorems.

Carroll symmetry in gravity and string theory

• Niels Obers (NORDITA)

Room: PI/1-100 - Theatre I will discuss the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. The leading order in the expansion leads to an action that corresponds to the electric Carroll limit of general relativity, of which I will highlight some interesting properties. The next-to-leading order will also be obtained, which exhibits a particular subsector that correspond to the magnetic Carroll limit, which features a solution that describes the Carroll limit of a Schwarzschild black hole. The incorporation of a cosmological constant in the Carroll (or ultra-local) expansion will also be commented on. Finally, I will describe how Carroll symmetry and geometry arises on the world-sheet of certain limits of string theory sigma models.

Hamiltonian Gauge Theory With Corners I: General Theory

• Michele Schiavina (ETH Zurich)

Room: PI/1-100 - Theatre I will present an analysis of the Hamiltonian formulation of gauge theories on manifolds with corners in the particular, yet common, case in which they admit an equivariant momentum map. In the presence of corners, the momentum map splits into a part encoding “Cauchy data” or constraints, and a part encoding the “flux” across the corner. This decomposition plays an important role in the construction of the reduced phase space, which then becomes an application of symplectic reduction in stages for local group actions. The output of this analysis are natural "corner" Poisson structures, leading to the concept of (classical) flux superselection sectors as their symplectic leaves. This is based on a collaboration with A. Riello. My talk will cover the general framework of corner superselection, while Riello’s talk will deal with its application to null boundaries and soft charges.

Avoiding the Corners: Partition Functions of Abelian Chern-Simons Theories on Handlebodies

• Massimo Porrati (New York University)

Room: PI/1-100 - Theatre This talk reviews the use of radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. By requiring that the only singularities of the gauge field inside the handlebody must be compatible with Wilson loop insertions, we find that the Wilson loop shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique state in the Hilbert space obtained from a Kähler quantization of the theory on the constant-radius Riemann surfaces. Radial quantization allows us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we show that our method reproduces the known partition function and Wilson loop VEVs at genus one.

Orbit Analysis of Corner Symmetries

• Robert Leigh (University of Illinois at Urbana-Champaign)

Room: PI/1-100 - Theatre Corner symmetries are those diffeomorphisms that become physical in codimension two, in that they support non-zero Noether charges. Recently we have shown how to extend phase space so that all such charges are integrable and give a representation of the corner symmetry algebra on this extended phase space. More recently we have studied the coadjoint orbits of what we now call the universal corner symmetry. One finds that certain complementary subalgebras, the extended corner symmetry and the asymptotic corner symmetry, can be associated with finite-distance and asymptotic corners, respectively. There is a simple geometric interpretation here in terms of an Atiyah Lie algebroid over a corner, whose structure group is the universal corner symmetry. The local geometry of a classical spacetime is encoded in related geometric structures.

Towers of soft operators and celestial holography

• Ana Maria Raclariu (Perimeter Institute)

Room: PI/1-100 - Theatre The tree-level soft theorems were recently shown to arise from the conservation of infinite towers of charges extracted from the asymptotic Einstein equations. There is evidence this tower promotes the extended BMS algebra to an infinite higher-spin symmetry algebra. In this talk I will introduce towers of canonically conjugate memory and Goldstone operators, highlighting their role in parameterizing the gravitational phase space. I will discuss the conditions under which these towers provide a complete set of scattering states and demonstrate that they are the building blocks of both soft and hard charges. I will finally show that the tower of tree level soft symmetries can be used to extend the Dirac (Faddeev-Kulish) dressings to include the infinite towers of Goldstones and comment on their implications for the gravitational S-matrix.

Matrix quantization of gravitational edge modes

• Antony Speranza (University of Illinois at Urbana-Champaign)

Room: PI/1-100 - Theatre The phase space of gravity restricted to a subregion bounded by a codimension-2 corner possesses an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and local SL(2,R) transformations of the normal planes. I will describe a deformation of a subalgebra preserving an area form on the sphere, and show that it leads to the finite dimensional algebra SU(N,N), reminiscent of older results concerning the fuzzy sphere, in which area-preserving diffeomorphisms are deformed to SU(N). This deformation is conjectured to be relevant to the quantization of the local gravitational phase space, and I will further demonstrate that the representation of SU(N,N) appearing in the quantization can be determined by matching the Casimir operators of the deformed algebra to classical phase space invariants. Based on 2012.10367 and upcoming work with W. Donnelly, L. Freidel, and S.F. Moosavian.

The partial Bondi gauge

• Marc Geiller (École Normale Supérieure de Lyon)

Room: PI/1-100 - Theatre I will review the recent construction of an extended solution space for gravity, based on a so-called partial Bondi gauge fixing. This aims at investigating the possible relaxations of the boundary conditions, in order to include for example a cosmological constant, a polyhomogeneous expansion, and an arbitrary time-dependent boundary metric. I will also explain how to properly map these results to the Newman-Penrose formalism. Finally, I will discuss the application to three-dimensional gravity, where a new asymptotic symmetry can be revealed after working out all the subtleties of the covariant phase space formalism.

BMS fluxes from every corner

• Laura Donnay (Technische Universität Wien)

Room: PI/1-100 - Theatre In this talk, I will present an updated account on the prescription for BMS fluxes in asymptotically flat spacetimes, including their split into hard and soft pieces and the associated symplectic structure. Implications for flat space holography will be discussed.

Celestial higher spin charges and gravitational multipole moments

• Ali Seraj (Universite Libre de Bruxelles)

Room: PI/1-100 - Theatre In this talk, I will describe celestial higher spin charges as corner integrals, and their relationship with gravitational multipole moments. I will then explain that these charges uniquely label gravitational vacua and the corresponding flux-balance equations describe the transition caused by gravitational radiation among different vacua. This tak is based on arXiv:2206.12597.

Conformal Carroll Scalar Actions

• Gerben Oling (NORDITA)

Room: PI/1-100 - Theatre I will construct explicit actions that are invariant under BMS/conformal Carroll symmetries. Over the last few years, we have developed a systematic procedure for constructing non-Lorentzian theories from limits and expansions of Lorentzian theories. To obtain explicit examples of candidate dual field theories for flat space holography, I apply this procedure to the conformally coupled scalar action, which leads to two classes of actions that are invariant under conformal Carroll symmetries. Time permitting, I will briefly mention ongoing work on the computation and classification of Weyl anomalies in such theories.

Horizons, fluid and what non-linearities might await

• Luis Lehner (Perimeter Institute)

Room: PI/1-100 - Theatre We analyze, first from a geometric point of view, the behavior of dynamical horizons. We then connect with Carrolian fluids and discuss potential phenomena stemming from non-linearities in the resulting equations [This is joint work with Jaime Redondo Yuste]

Cutting Corners with Celestial CFT

• Sabrina Pasterski

Room: PI/1-100 - Theatre Celestial Holography proposes a duality between gravitational scattering in asymptotically flat spacetimes and a conformal field theory living on the celestial sphere. The main motivation for this program comes from the connection between soft theorems and asymptotic symmetries in asymptotically flat spacetimes, and our ability to recast soft operators as currents in a codimension 2 CFT. We present a streamlined route from asymptotic symmetries in 4D asymptotically flat spacetimes to currents in a 2D celestial CFT in a manner that makes their relation to QFT soft theorems manifest. We use this to re-examine the bulk picture of radial evolution in the 2D theory and reconcile the construction of charges in CCFT with the more familiar construction from AdS/CFT, despite the differing codimension. In the process, we point out how the Carrollian and Celestial perspectives amount to slicing the bulk and boundary in different ways — our celestial slices cut through the usual corner! — and emphasize how these perspectives inform each other. Based on 2201.06805, 2202.11127 and 2205.10901

A Celestial Matrix Model

• Charles Marteau (University of British Columbia)

Room: PI/1-100 - Theatre We construct a Hermitian random matrix model that provides a stable non-perturbative completion of Cangemi-Jackiw (CJ) gravity, a two-dimensional theory of black holes in asymptotically flat spacetimes. The matrix model reproduces, to all orders in the topological expansion, the Euclidean partition function of CJ gravity with an arbitrary number of boundaries. The non-perturbative completion enables the exact computation of observables in flat space quantum gravity which we use to explicitly characterize the Bondi Hamiltonian spectrum. We discuss the implications of our results for the flat space S-matrix and black holes.

Asymptotic algebra of quantum electrodynamics from the BV-BFV perspective

• Kasia Rejzner (University of York)

Room: PI/1-100 - Theatre This talk focuses on classical features of asymptotic QED, i.e. the limit of QED at null and time-like infinity. The BV-BFV formalism allows one to view this as a boundary theory of bulk QED and carries a natural notion of what it means to be a symmetry of the model. I will make the connection between this perspective and the earlier findings of Herdegen (JMP 1996) and Strominger et.al. (JHEP 2014) concerning large gauge symmetries in QED. This is based on a joint paper with Michele Schiavina (CMP 2021).

Geometric actions for BMS4

• Glenn Barnich (Universite Libre de Bruxelles)

Room: PI/1-100 - Theatre After reviewing the constrained Hamiltonian analysis of geometric actions, the construction is applied to the case of the BMS group in four dimensions, where it yields two plus one dimensional BMS4 invariant field theories. (Based on work done in collaboration with K. Nguyen and R. Ruzziconi)

Hamiltonian Gauge Theory With Corners II: memory as superselection in null YM theory

• Aldo Riello (Perimeter Institute)

Room: PI/1-100 - Theatre On Tuesday, M. Schiavina laid out the theoretical framework for the symplectic reduction of gauge theories in the presence of corners. In this talk I will apply this theoretical framework to Yang-Mills theory on a null boundary and show how a pair of soft charges controls the residual (corner) gauge symmetry after the first-stage symplectic reduction, and therefore the superselection structure of the theory after the second-stage symplectic reduction. I will also discuss the subtleties of the gauge A_u = 0, the interpretation of electromagnetic memory as superselection, and how the nonlinear structure of the non-Abelian theory complicates this picture.

Flat asymptotics, charges and dual charges -- what the Cotton can do

• Marios Petropoulos (Ecole polytechnique - CNRS)

Room: PI/1-100 - Theatre In this talk I will explore the role of the boundary Cotton tensor in the reconstruction of the solution space of four-dimensional asymptotically AdS and mostly asymptotically flat spacetimes. I will discuss charges from a purely boundary perspective, which emerge in sets of electric and magnetic towers, not necessarily conserved and possibly including subleading components.

Carrollian spaces at infinity: an embedding space picture

• Jakob Salzer (Université Libre de Bruxelles)

Room: PI/1-100 - Theatre In this talk, I will discuss certain homogeneous spaces of the Poincaré group that correspond to the well-known asymptotic regions of asymptotically flat spacetimes: time-, space-, and light-like infinity. I will then show that all of these spaces admit a uniform description as surfaces embedded in a higher-dimensional space. I will conclude with some comments concerning the computation of correlators of conformal carrollian theories from this embedding space picture.

Wald-Zoupas vs. improved Noether charge: anomalies as soft terms at scri

• Simone Speziale (Centre de Physique Théorique)

Room: PI/1-100 - Theatre In the last few years, various authors have extended the covariant phase space to include arbitrary anomalies, and a notion of improved Noether charge. After reviewing this construction and discussing examples of anomalies, I will point out that the covariance requirements of the seminal Wald-Zoupas paper permit the presence of a special class of anomalies. To illustrate the meaning of such anomalies, one can look at the case of future null infinity where they take the form of the soft terms in the flux-balance laws.

Conclusive Remarks

• Luca Ciambelli (Perimeter Institute)
• Celine Zwikel (Perimeter Institute)

Room: PI/1-100 - Theatre