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.
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.
The AdS/CFT correspondence (Anti-de Sitter gravity/ conformal field theory correspondence), also referred to as holography, provides the first example of a duality relating a gravity theory to a quantum field theory without gravity. The gravity theory involved describes the hyperbolic bulk spacetime and the quantum field theory its boundary. This duality has its origin within string theory. Recent developments based on both quantum information theory and the physics of black holes raise the question if dualities of this type exist more generally, even beyond string theory. As a specific example, I will describe recent progress towards establishing a duality based on a discretisation of hyperbolic Anti-de Sitter space that is obtained by a regular tiling with polygons. I will explain how to obtain a dual Hamiltonian on the boundary that reflects properties of the bulk tiling, and describe its properties. This research direction is related to recent developments in mathematics, quantum information, condensed matter physics and electrical engineering, making it truly interdisciplinary. I will conclude by giving an outlook on the next steps to be followed in view of obtaining a full discrete duality.
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.
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 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.
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.
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.
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.
Based on arXiv:2208.04334. We consider oscillons - localized, quasiperiodic, and extremely long-living classical solutions in models with real scalar fields. We develop their effective description in the limit of large size at finite field strength. Namely, we note that nonlinear long-range field configurations can be described by an effective complex field ψ(t, x) which is related to the original fields by a canonical transformation. The action for ψ has the form of a systematic gradient expansion. At every order of the expansion, such an effective theory has a global U(1) symmetry and hence a family of stationary nontopological solitons - oscillons. The decay of the latter objects is a nonperturbative process from the viewpoint of the effective theory. Our approach gives an intuitive understanding of oscillons in full nonlinearity and explains their longevity. Importantly, it also provides reliable selection criteria for models with long-lived oscillons. This technique is more precise in the nonrelativistic limit, in the notable cases of nonlinear, extremely long-lived, and large objects, and also in lower spatial dimensions. We test the effective theory by performing explicit numerical simulations of a (d+1)-dimensional scalar field with a plateau potential.
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.