Quantum Gravity Around the Corner

Oct 3, 2022, 8:30 a.m. → Oct 7, 2022, 5:15 p.m. America/Toronto

PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

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

There has been recent activity in looking for new conserved charges and symmetries in gravity, most notably at infinity but also for finite regions. An important question is whether some of these charges and symmetries have physical implications. These charges are evaluated on codimension-2 surfaces  called corners, which constitute the main focus of this conference. The goal is to bring together leading experts and promote discussions and exchanges among different approaches to (quantum) gravity. 

https://pirsa.org/C22029

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land. 

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

Monday, October 3

9:30 a.m. Registration

1 Welcome & Opening Remarks

Speakers: Celine Zwikel (Perimeter Institute), Luca Ciambelli (Perimeter Institute)

2 Review Talk: A primer on the covariant phase space formalism

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.

Speaker: Adrien Fiorucci (Technische Universität Wien)

Adrien Fiorucci Review Talk.docx

10:55 a.m. Break

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

Speaker: Adrien Fiorucci (Technische Universität Wien)

12:00 p.m. Lunch

4 Review Talk: An introduction to coadjoint orbits

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.

Speaker: Andrea Campoleoni (University Of Mons)

Andrea Campoleoni Review Talk.docx

2:25 p.m. Break

5 Review Talk: An introduction to coadjoint orbits cont.

Speaker: Andrea Campoleoni (University Of Mons)

3:30 p.m. Coffee Break

6 Gong Show

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

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

5:30 p.m. Wine & Cheese Reception

Tuesday, October 4

7 Local Holography and corner symmetry: A paradigm for quantum gravity

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: Laurent Freidel (Perimeter Institute)

8 Residual gauge symmetries in the front form

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.

Speaker: Sucheta Majumdar (École Normale Supérieure de Lyon)

10:30 a.m. Coffee Break

9 Carrollian Perspective on Celestial Holography

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.

Speaker: Romain Ruzziconi (Technische Universität Wien)

10 Carroll symmetry in gravity and string theory

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.

Speaker: Niels Obers (NORDITA)

12:30 p.m. Lunch

11 Hamiltonian Gauge Theory With Corners I: General Theory

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.

Speaker: Michele Schiavina (ETH Zurich)

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

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.

Speaker: Massimo Porrati (New York University)

3:45 p.m. Coffee Break

Wednesday, October 5

13 Orbit Analysis of Corner Symmetries

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.

Speaker: Robert Leigh (University of Illinois at Urbana-Champaign)

14 Towers of soft operators and celestial holography

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.

Speaker: Ana Maria Raclariu (Perimeter Institute)

10:30 a.m. Coffee Break

15 Matrix quantization of gravitational edge modes

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.

Speaker: Antony Speranza (University of Illinois at Urbana-Champaign)

16 The partial Bondi gauge

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.

Speaker: Marc Geiller (École Normale Supérieure de Lyon)

12:30 p.m. Lunch

Thursday, October 6

17 BMS fluxes from every corner

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.

Speaker: Laura Donnay (Technische Universität Wien)

18 Celestial higher spin charges and gravitational multipole moments

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.

Speaker: Ali Seraj (Universite Libre de Bruxelles)

10:30 a.m. Coffee Break

19 Conformal Carroll Scalar Actions

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.

Speaker: Gerben Oling (NORDITA)

20 Horizons, fluid and what non-linearities might await

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]

Speaker: Luis Lehner (Perimeter Institute)

12:30 p.m. Lunch

21 Cutting Corners with Celestial CFT

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

Speaker: Sabrina Pasterski

22 A Celestial Matrix Model

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.

Speaker: Charles Marteau (University of British Columbia)

3:45 p.m. Coffee Break

23 Asymptotic algebra of quantum electrodynamics from the BV-BFV perspective

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).

Speaker: Kasia Rejzner (University of York)

Friday, October 7

24 Geometric actions for BMS4

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)

Speaker: Glenn Barnich (Universite Libre de Bruxelles)

10:30 a.m. Coffee Break

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

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.

Speaker: Aldo Riello (Perimeter Institute)

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

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.

Speaker: Marios Petropoulos (Ecole polytechnique - CNRS)

12:30 p.m. Lunch

27 Carrollian spaces at infinity: an embedding space picture

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.

Speaker: Jakob Salzer (Université Libre de Bruxelles)

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

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.

Speaker: Simone Speziale (Centre de Physique Théorique)

29 Conclusive Remarks

Speakers: Celine Zwikel (Perimeter Institute), Luca Ciambelli (Perimeter Institute)

4:00 p.m. Coffee Break