Higher spin symmetry in gravity and Yang-Mills

In this talk I'll review the construction from phase space of a tower of asymptotic charges in gravity and yang-mills that includes for gravity the mass aspect, the angular momentum aspect and a tower of similar higher spin charges. I will show that they generate a canonical algebra which provides a non-linear generalization of LW_{\infty} when the shear doesnt not vanish. I will also present how this construction provides a new perspective on the connection between asymptotic infinity and twistor theory.

Celestial OPE: w_{1+∞} and beyond

Celestial holography aims at establishing a duality between gauge/gravity theories in the bulk of asymptotically flat spacetimes and a celestial CFT on the sphere at null infinity. However in order to have a fully fledged duality we need to better understand the properties that define the boundary CFT and the OPE makes for an important part of the problem. Strominger et al. showed that the singular part of the celestial OPE can be obtained from the leading order splitting function in the collinear expansion and this unraveled the w_{1+∞} algebra that was hiding in the soft sector of gravity. In this talk we will prove that this algebra is free from ambiguity by investigating the antisymmetric double soft graviton limit and showing that it vanishes. Furthermore we will discuss the structure of the full soft graviton OPE (including regular terms), the spectrum of primaries that appears as well as their descendants.

BMS particles

Wavefunctions for unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group are constructed. They are shown to describe, in general, quantum superpositions of (Poincaré) particles propagating on inequivalent gravity vacua. This follows from reconsidering McCarthy’s classification of BMS group UIRs through a unique, Lorentz-invariant but non-linear, decomposition of supermomenta into hard and soft pieces.

Thoughts on asymptotic renormalisation

Asymptotic gravitational symmetries are a powerful probe of the holographic principle. Unlike pure gauge transformations, they carry non‑vanishing conserved charges at the boundary. However, as one approaches this boundary, the quantities that define these charges may diverge, making a renormalization procedure essential. While holographic renormalization is well understood for asymptotically AdS spacetimes, its flat‑space counterpart remains elusive. In this talk I will give an overview of the AdS program, then survey what is known in asymptotically flat backgrounds via the linearized theory for arbitrary spin in any dimension. I will highlight the key open questions that should be addressed to elucidate the putative dual CFT, and invite discussion on these directions.

Lessons for Celestial Holography from AdS-CFT

The holographic principle provides our best toy model of quantum gravity in asymptotically Anti de Sitter spaces. Attempts to generalise these ideas to more physically meaningful backgrounds with positive or vanishing cosmological constants have so far been at odds with their radically different asymptotic structure. In this talk I will review recent efforts in this direction which are centred on reformulating physics both in flat and dS space in terms of physics in Euclidean AdS space. I will try to argue that this reformulation will allow to concretely use some of the most powerful tools of AdS-CFT to harness the holographic principle beyond AdS space.

Canonical realization of BMS$_4$ algebra. A celestial interpretation

We construct the canonical canonical realization of BMS$_4$ in terms of the Fourier modes of a 4d massless free Klein-Gordon field expressed in terms of celestial coordinates. The role of one of the two quadratic Lorentz Casimir generators in the construction of the realization is emphasized. We also construct the w infinity algebra that generalizes the superrotations.

A Carrollian perspective on gravitational multipoles

After a review on Carroll geometry in Cartan's frame, with emphasis on the construction of charges and the study of their conservation, I will present how one can build two towers of charges in the context of asymptotically flat Petrov-algebraically special spacetimes. The two towers are built upon the Carrollian equivalent of the energy-momentum (electric tower) and Cotton tensor (magnetic tower). Taking for simplicity the example of Kerr-Taub-NUT, I will show that the electric tower reproduces the gravitationnal multipole as defined by Geroch and Hansen in the 70s.

Asymptotic fluxes in holography

Asymptotic charges associated with asymptotic spacetime symmetries play a key role in holographic dualities. The aim of this talk will be to discuss the generalisation to asymptotic fluxes. We will begin by discussing the analysis of such fluxes in the context of asymptotically locally anti de Sitter and de Sitter spacetimes, where such fluxes capture radiative effects. We identify the conservation laws for these fluxes, illustrating these in the context of various examples and explain their physical interpretations. We will then consider the case of asymptotically flat spacetimes, and explain how the conversation laws at finite lambda link to asymptotically flat holography.

Debate on quadrupole formula in de Sitter

It is well-known that gravitational fields from an isolated system depend on the time varying quadrupole moment of the source. Quadrupole formula provides an estimate of the energy loss due to gravitational radiation. The first proposed quadrupole formula for gravitational waves in de Sitter was derived by Ashtekar, Bonga, Kesavan (ABK). We point out that a consistent quadrupolar truncation is needed to upgrade the ABK formula. We also compare our result to a recently obtained result of Bonga, Bunster, Perez. We write the quadrupole formula in two distinct ways which allow standard flat limit and negative definite energy flux in de Sitter. The existence of several proposals for the quadrupole formula suggests that fundamental requirements on the uniqueness of the quadrupole formula, such that the enforcement of gauge invariance, are still missing.

High-energy string theory, celestial holography and tensionless strings

In my talk I make connection between three seemingly unrelated topics: (a) the high energy limit of string theory (more specifically, the high energy (zero tension) limit of tree-level string scattering in flat backgrounds) and its subleading corrections as saddle-point approximation on the string world-sheet, (b) the infinite energy limit of celestial amplitudes as stationary phase approximation and (c) amplitudes of tensionless (null) strings and the role of open and closed strings.

Infrared divergences of gravitational scattering and BMS representations

I will discuss soft theorems from the perspective of representations theory of the BMS group and explain why they forces us to consider states which are non standard BMS representations. I will then present new results on the physical interpretation, as well as explicit descriptions, of these new states lying outside of the usual Fock space. This is based on a common work with X. Bekaert and L. Donnay.

Topological strings on the beach

The KP equation is a well-known classical integrable system that describes shallow water waves in 2+1 dimensions. Perhaps surprisingly, it can also be seen as an example of Celestial Holography and comes complete with a chiral W-algebra which may be seen both via collinear limits of form factors and via defects in twistor space. I’ll construct a 5d mixed topological-holomorphic Chern-Simons theory that explains all this, and shows how solitonic solutions of the KP equations correspond to holomorphic line bundles on non-commutative mini-twistor space.

Null Physics: What'd I Miss?

The last decade has experienced a surge of interest in the understanding of physics on null hypersurfaces. From black hole horizons to flat space holography and causal diamonds, passing through the mastery of degrees of freedom and quantization of gravity on a generic finite distance null hypersurface, a unified framework has been put forward. In this talk, we will review the salient latest developments, focusing on the following main achievements. 1) Geometry and conservation laws of a null hyper 2) Gravitational phase space, symmetries, and quantization 3) Asymptotic limit to null infinity, and extended BMS anomalies 4) Quantum informational derivation of entropy bounds on black hole horizons 5) Quantum area fluctuations of a causal diamond.

Quantizing Carrollian field theories

Carrollian field theories have recently emerged as a candidate dual to flat space quantum gravity. In this talk, I will discuss the quantization of generic two-derivative electric and magnetic Carrollian theories, highlighting some of the subtleties involved in this process. We will also explore simple examples of interacting theories that couple electric and magnetic sectors with a tractable perturbative expansion. As another concrete application, I will present the partition function of a two-dimensional BMS3​-invariant field theory, which captures the boundary degrees of freedom of three-dimensional flat space gravity. I will conclude with potential lessons for the program of flat space holography from the carrollian point of view.

Emergent Translation Invariance in Celestial Holography

While natural from a bulk point of view, four-dimensional translation invariance acts unfamiliarly on the celestial CFT and forces low-point massless celestial amplitudes to be distributional. This provides a challenge to constructing simple examples where a 2D CFT computes 4D amplitudes. In this talk, we discuss how translation invariance scattering amplitudes can be extracted from combinations of CFTs with only Lorentz symmetry by showing that distributional celestial amplitudes can emerge from linear combinations of smoother correlation functions. Additionally, we show that translation invariance can emerge from entanglement between two systems without fundamental translation invariance.

Decoding Celestial Holography

Is there a lattice analog of celestial CFT? How would IR effects manifest and emerge in its continuum limit? In this talk we devise a Quantum Error Correcting (QEC) framework to encode both effects. We will show how to embed a chain of qudits in Klein spacetime and then take its continuum N →∞limit. Here hard states with quantized BMS hair in the celestial torus form the logical subspace, robust under errors induced by soft radiation. Time permitting, we comment on the relation to noncommutative spacetimes, the w1+∞hierarchy of soft currents and its realization from a sigma model in twistor space.

Theory of Carroll Flux-Balance Laws for Flat-Space Holography

The main challenges in formulating a holographic correspondence for asymptotically flat spacetimes stem from the null nature of the conformal boundary and the non-conservation of gravitational charges in the presence of bulk radiation. In this talk, I shall present the systematic and mathematically robust approach to understanding and deriving the associated flux-balance laws from geometric principles defined intrinsically at the boundary.
I shall begin by reviewing key aspects of the geometry at null infinity, known as conformal Carroll geometry. I shall highlight that the boundary affine connections contain degrees of freedom that naturally act as sources encoding radiation in a holographic framework. I shall then derive flux-balance laws for an effective field theory formulated at the boundary, using novel techniques that introduce "hypermomenta" as the responses to fluctuations in the boundary connection. These equations reproduce the celebrated BMS flux-balance laws in a convenient boundary gauge.

Amplitudes and Asymptotic Symmetries

I will give an overview of loop scattering amplitudes in field theory and string theory inspired by SCET (soft collinear effective field theory), following Hannesdottir and Schwartz. The purpose is to invite discussion of how amplitude implementations of infrared symmetries fit in the big picture of asymptotic symmetries.

Global symmetries and the affine connection

It has been recently realised that in certain non-lorentzian limits the affine connection emerges as an independent external source in holographic systems. In that sense, its presence is intimately related to the global symmetries of the matter system. As a further example of this general phenomenon I show that coupling matter fields to an affine connection allows us to give a geometric interpretation of the well-known improvement terms of the energy momentum tensor. I will provide a few concrete examples in simple fields theories of scalar, fermion and gauge fields, as well as more complicated examples of higher derivative theories. A holographic picture of metric affine gravity will be briefly discussed.

Carroll Approximations of General Relativity, BKL Dynamics and Holography

What goes on behind the horizon of black holes? A long time ago, general relativity was conjectured to lead to chaotic dynamics in the vicinity of spacelike singularities. Recently, it was observed that this so-called BKL dynamics, which features ‘bounces’ between Kasner geometries, can be engineered in AdS black holes in a relatively straightforward way using relevant deformations in the dual CFT. However, extracting predictions from Einstein gravity in this near-singularity regime remains extraordinarily challenging, which limits our understanding of the validity and generality of BKL limits as well as their holographic interpretation in AdS/CFT. In this talk, I will present a novel approach to the challenges of near-singularity dynamics using ultra-local geometric Carroll approximations of gravity.

Boundary structure of local gauge theories

I plan to review the BV-AKSZ approach to local gauge theories with boundaries, based on representing a gauge theory as a so-called gauge PDE. In this approach the geometrical structure defining the theory can be pulled back to a spacetime submanifold, giving a local gauge theory defined therein. In the case of boundary, the induced gauge theory is referred to as boundary structure and can be thought of as a gauge-invariant and coordinate-free definition of the data induced on the boundary. The example of asymptotically AdS/flat gravity + matter is discussed. If time permits, I also plan to comment on the relation to the covariant phase space approach.

Gravitational Radiation and Charges on de Sitter

We write a closed form expression for the metric perturbation around de Sitter that describes gravitational radiation from a compact and slowly varying source, in terms of a consistent multipolar expansion at quadrupolar order. We show that the corresponding displacement memory effect with both the even and odd parities is at a higher order in the radial expansion compared to their flat counter-parts. Using the form of the metric perturbation we obtained, we write expressions for SO(1,4) charges at future infinity that reduce to the correct expressions in the flat limit, which also includes a definition of mass that strictly decreases in the presence of gravitational radiation.