Classical observables of General Relativity from scattering amplitudes

I will be using scattering amplitudes, instead of the Lagrangian of General Relativity (GR), to compute classical observables in GR. In the first part of the seminar I will consider the elastic scattering of two massive particles, describing two black holes, and I will show how to compute the eikonal up to two-loop order, corresponding to third Post-Minkowskian (3PM) order, that contains all the classical information. From it I will compute the first observable that is the classical deflection angle. In the second part of the seminar I will be computing the resummed soft waveform following the approach of Weinberg from 1965. Then, if I have time left, in the third part of the seminar, I will consider inelastic processes with the emission of soft gravitons. In this case the eikonal becomes an operator containing the creation and annihilation operators of the gravitons. The case of soft gravitons can be treated following the Bloch-Nordsieck approach and, in this case, I will be computing two other observables: the zero-frequency limit (ZFL) of the spectrum dE/d\omega of the emitted radiation and the angular momentum loss at 2PM and 3PM. I will consider also the case in which there are static modes localised at $\omega=0$. Finally, I will study the high energy limit. In particular, since the graviton is the massless particle with the highest spin, we expect universality at high energy in any gravitational amplitude. I will show that universality at high energy is satisfied both in the elastic and inelastic case, but this happens in the inelastic case in a very non trivial way. I will end with some conclusions and with a list of open problems.

Celestial symmetry charges from holography, twistor space and null infinity

This talk explains the interrelationship between three theories of the the soft symmetries discovered by Strominger et.al. focussing on the case of Yang-Mills. These were originally discovered from an OPE that arises from universal properties of Yang-Mills and gravitational amplitudes in their collinear limits. These have been understood as vertex operators for (ambi)-twistor-strings, charges at null infinity by Friedel-Pranzetti & Raclariu and top-down celestial Holography by Costello-Paquette. We give a unified presentation from the perspective of twistor actions in the asymptotic twistor space associated to null infinity where they tie into the theory of integrable hierachies for the self-duality equations and their recursion operator as discovered in the 90's. This is joint work with Adam Kmec, Romain Ruzziconi and Atul Sharma arxiv:2506.01888.

Gravitational Waveforms, Soft Theorems and Soft Spectra

Scattering amplitudes provide a convenient strategy to calculate gravitational-wave observables characterizing compact binaries in the weak-field or post-Minkowskian (PM) regime, when the two objects remain far away from each other. Conversely, classical soft theorems encode exact information about the dynamics of such systems and do not rely on the PM expansion, while of course restricting to the low-frequency band of the gravitational wave spectrum. In this talk I will illustrate recent progress on these two complementary approaches to the gravitational two-body problem, focusing in particular on new predictions for the waveforms, the radiated energy spectrum and the angular momentum loss.

A notion of spin for asymptotically-flat spacetimes

Defining a notion of spin in the presence of gravity is a long-standing question in classical gravitational physics. In this talk, I will propose a definition of spin for asymptotically-flat spacetimes by leveraging the framework of asymptotic symmetries and the method of coadjoint orbits. I will argue that the appropriate asymptotic symmetries to approach this problem is the generalized BMS (gBMS) algebra. I will then discuss the moment map for the action of gBMS algebra, which allows the construction of spin charge on a gravitational phase space. By applying the construction to the case of Kerr black hole, I will explain how its mass, angular momentum, and hence all its multiple moments, can be computed in terms of Casimir functionals associated with the coadjoint orbits of gBMS algebra. I conclude with some of the most interesting questions left to be explored. This talk is based on joint work with Laurent Freidel and Daniele Pranzetti (arXiv:2403.19547).

Connecting Shockwaves and Memories

We study the infrared on-shell action of Einstein gravity in asymptotically flat spacetimes, obtaining an effective, gauge-invariant boundary action for memory and shockwave spacetimes. We show that the phase space is in both cases parameterized by the leading soft variables in asymptotically flat spacetimes. We then demonstrate that our on-shell action is equal to three quantities studied separately in the literature: (i) the soft supertranslation charge; (ii) the shockwave effective action; and (iii) the soft effective action.

Lorentz covariant supertranslation frames for the angular momentum aspect

I review the well known ambiguity in defining angular momentum (and mass dipole) fluxes in general relativity and reinterpret recent works that resolve the ambiguity by defining invariant charges. The ambiguity is resolved by finding the conditions that fix a frame for supertranslation and for space-time translation. I also present an elementary method for measuring the rotational part of the angular momentum aspect.

More details on the non-linear memory effect of Robinson-Trautman waves

The memory effect for Robinson-Trautman waves is explicitly worked out. In a first step, we apply the combined frame rotation and coordinate transformation that make Robinson-Trautman waves asymptotically flat. This allows us to use well-established results on how to derive the memory effect in this context. The local mass-loss formula for the generalized mass aspect, which is shown to be manifestly positive, provides a new formulation of the Robinson-Trautman evolution equation. The no-news sector of the theory is identified with the vacuum sector of Euclidean Liouville theory and contains the boosted Schwarzschild black hole.

Into deep IR on deS

I will discuss the scattering processes in global de Sitter spacetime from the perspective of inertial observers. I will consider the processes in which IR decouples from UV as well as some generic features of deep IR physics.

Celestial vs. Carrollian symmetries

I will compare the celestial and Carrollian approaches to constructing Noether charges for asymptotic symmetries. In the former case, one works with chiral currents of celestial CFT, while in the latter case, one introduces corner charges. Working in the context of self-dual Yang-Mills theory, I will discuss how the charge aspects recently constructed by Freidel, Pranzetti and Raclariu (FPR) provide the common building blocks of both corner charges and celestial currents. FPR's higher-spin extensions of asymptotic Bianchi identities allow us to prove the holomorphicity of celestial currents and the conservation of corner charges under the same conditions of absence of radiation.

Categorification of the Giant Graviton expansion

The Giant Graviton expansion expresses a supersymmetric index of a U(N) gauge theory as a series of corrections to the large N result. I will discuss combinatorial and holographic interpretations of individual terms in the expansion, in terms of trace relations and families of Giant Graviton branes. This is based on ongoing collaborations with Davide Gaiotto and Matthew Heydeman.

Carroll theories from Lorentzian light-cone actions

Light-cone Minkowski spacetime, comprising two null coordinates, is one of the simplest examples of a Bargmann manifold. By deforming the Lorentzian light-cone action in (d+1) dimensions, we derive d-dimensional Carroll theories via null reduction from Bargmann spacetimes. While the magnetic Carroll sector can be directly obtained from the relativistic parent action, the deformation is essential for obtaining the electric Carroll sector. We, thus, argue that the magnetic Carroll sector represents a consistent truncation of the relativistic parent theory in one higher dimension. For theories with gauge symmetry, we highlight the role of the light-cone gauge condition in the Carrollian dynamics.

Celestial amplitudes for strings, and universal structure of IR divergences in nonabelian gauge theory on the celestial sphere

This will be a review talk of recent and earlier results on celestial amplitudes in field and string theory, including loop corrections. We will first see how, in nonabelian SU(N) gauge theory, the universal soft/collinear factorization (valid to all-loop order) persists for celestial correlators and allows one to describe its infrared structure (in the large N limit) in terms of vertex operators in a Coulomb gas of colored scalars with nearest-neighbor interactions. We also show how 1/N corrections point toward a description of the IR sector in terms of deviations from the Knizhnik-Zamolodchikov equation. For strings, we review celestial amplitudes for open and closed strings, at tree and one-loop levels, studying also the extreme regimes of low and high energy limits. For the latter, a map between the worldsheet CFT and the CCFT seems to emerge.

Detection prospects of gravitational-wave memory effects from binary-black-hole mergers

The gravitational-wave (GW) memory effect is characterized by a persistent offset in the GW strain, which is closely related to the subtle infrared physics of asymptotically flat spacetimes. There are ongoing searches for the memory effect from GW observations of binary black holes by the LIGO-Virgo-KAGRA collaboration and by pulsar timing arrays, including NANOGrav. I will discuss how these detectors search for the memory effect and what aspects of the memory effect and soft gravitational physics can be probed by them. The memory effect is just the leading-order persistent GW effect in a hierarchy of "higher GW memory effects" that are related to multiple time integrals of the news tensor (the radiative degrees of freedom in asymptotically flat spacetimes). The next order contains the drift memory effects, also called the spin and center-of-mass memory effects; one order higher are the ballistic memory effects. I also will discuss the definitions of these higher memory effects, the features of the GW strain related to these effects in post-Newtonian and numerical-relativity calculations of binary black hole mergers, and their detection prospects.

Memory, Infrared Entanglement, and the Idealization of Scattering from Infinity

The memory effect refers to the fact that in four dimensional asymptotically flat spacetimes, at order 1/r a massless field generically will not return to the same value at late retarded times as it had at early retarded times. In electromagnetism and gravity, when memory is present, the late retarded time field will differ from the early retarded time field by an asymptotic symmetry. There is a direct relationship between memory and the charges that generate the asymptotic symmetries. These charges must commute with any gauge invariant local observables in the bulk spacetime, thereby effectively decohering bulk states into superselection sectors of eigenstates of the large gauge charges. It can thereby be seen that in QED, states corresponding to "incoming bare electrons" from infinity (i.e., electron states with no incoming electromagnetic radiation) do not correspond to physical states in the bulk. The physical bulk states correspond at infinitely early and late times to Faddeev-Kulish states, in which the electrons are infinitely entangled with soft photons so as to produce eigenstates of the large gauge charges. However, for a physical bulk state, this entanglement will occur only logarithmically in time and should be completely negligible in the finite time required to do any realistic experiment in the bulk. In QED with massless charged particles, the Faddeev-Kulish construction yields singular states, and it does not appear that quantum scattering theory from infinity makes sense at all (even though classical scattering theory is well defined). In gravity, there are no eigenstates of the large gauge charges (apart from the vacuum), but there also are no gauge invariant local bulk observables, so it is not obvious what criteria should be imposed on scattering states so that they correspond to physically relevant bulk states. In all cases, the behavior of states at asymptotic infinity is very different from the behavior of states at the large but finite times relevant to experiments in the bulk spacetime. Although the idealization of scattering theory from infinity can be very usefully applied to various “practical calculations” (such as obtaining inclusive cross-sections), this work highlights that there are serious difficulties in elevating scattering from infinity to a fundamental status in the formulation of a theory.

Twisting asymptotically-flat spacetimes

I will present the detailed construction of an extension of the Bondi framework which includes a non-vanishing twist, i.e. the relaxation of the hyperspace-orthogonality condition. This extension has several advantages which have been noted in recent work. First, it allows to access a Carroll-covariant structure on Scri. Second, and most importantly, the presence of a non-vanishing twist allows to write all the algebraically special solutions in finite form. This includes for example Kerr or supertranslated Schwarzschild, which would otherwise require an infinite 1/r expansion when written in the standard non-twisting Bondi gauge. This opens the possibility of defining symplectic symmetries for these algebraically special solutions. The construction of the algebraically general solutions near null infinity requires the use of a combination of the Newman-Penrose and metric formalisms, which will be presented in detail.

Log soft theorems and asymptotic symmetries

Over the past decade, a remarkable connection has been established between soft theorems and the asymptotic symmetries of quantum field theories: soft theorems are the Ward identities of asymptotic symmetries. In particular, at tree level, subleading soft theorems correspond to the Ward identities of the subleading asymptotic symmetries of the theory — divergent gauge transformations in QED and superrotations in gravity. These soft theorems receive loop corrections, and Sahoo and Sen have shown that such corrections give rise to a novel, one-loop exact soft theorem with logarithmic dependence on the soft energy. This naturally raises the question: what is the symmetry interpretation of this log soft theorem? In this talk, we explore this question in the context of scalar QED and perturbative gravity. We show that log soft theorems are Ward identities of the subleading asymptotic symmetries, with long-range interactions properly taken into account.

Soft theorems and spontaneous symmetry breaking

The soft photon and soft graviton theorems of Weinberg are known to derive from conservation laws associated with asymptotic symmetries. Within the corresponding classical theories, one often speaks of spontaneous symmetry breaking and vacuum degeneracy, but a genuine quantum description of this phenomenon has largely been lacking. In this talk I will establish spontaneous breaking of asymptotic symmetries and the existence of Goldstone `particles' using exclusively the language of quantum field theory. This is made possible through the reformulation of massless scattering theory in terms of carrollian conformal field theory, and the observation that soft theorems correspond to Ward identities of broken symmetries. I will derive a version of Goldstone theorem which implies the existence of zero-momentum particles described by conformal fields on the celestial sphere.

Celestial Symmetries of Black Hole Horizons

I will present a novel correspondence between the gravitational phase space at null infinity and the subleading phase space for finite-distance null hypersurfaces, such as black hole horizons. Using Newman-Penrose formalism and an off-shell Weyl transformation, this construction transfers key structures from asymptotic boundaries to null surfaces in the bulk—for instance, a notion of radiation. Imposing self-duality conditions, I will identify the celestial symmetries and construct their canonical generators for finite-distance null hypersurfaces. This framework provides new observables for black hole physics.

Carrollian momenta from anti de Sitter

Defining an energy-momentum tensor for asymptotically flat spacetimes seems to be of interest in its own right, or for possible holographic applications. That said, the role it could play is less clear than for anti de Sitter, bearing in mind that in the flat case an infinite number of data are needed on scri to reconstruct a solution. I will show that besides the Carrollian geometric structure at null infinity, this infinite set dubbed Carrollian momenta emerge as the Laurent coefficients of the AdS energy-momentum tensor expanded in powers of the cosmological constant. The present analysis unravels the role of the boundary Cotton tensor.

Scalar Subleading Soft Expansion from an Infinite Tower of Conserved Charges

We investigate the emergence of infinite-dimensional symmetries in the absence of gauge invariance by analyzing massless scalar theories. Our approach constructs an infinite tower of charges derived from the most general subleading equations of motion at null infinity. These charges are defined by specific combinations of asymptotic field coefficients. By carefully examining the dynamics at spatial infinity, we demonstrate that this tower of surface integrals commutes with the S-matrix of the interacting model. Additionally, we discuss the potential holographic origin of these charges and briefly explore models that allow loop-level calculations.

Progress on the action approach to flat space asymptotic symmetries

I will discuss ongoing work on the formulation of flat space asymptotic symmetries in terms of the action with scattering boundary conditions. This provides an alternative perspective to the more standard canonical phase space approach. Applications to gauge theory and gravity will be discussed.

Boundary energy-momentum tensors for asymptotically flat spacetimes

Future null infinity is a Carrollian manifold. I will consider asymptotic solutions to the 4D vacuum Einstein equations where future null infinity is endowed with the most general Carroll metric that is allowed by the Einstein equations. I will show that the first few orders of the near-boundary expansion are organised in terms of connections that take values in the conformal algebra subject to a set of curvature constraints. I will also derive the Bondi loss equations for this general setup and show how they can be obtained from setting up a well-posed variational problem by adding counterterms to the Einstein-Hilbert action. The on shell variation of the renormalised action can be written in terms of responses to variations of the Carroll metric data and the shear. This leads to an energy-momentum-news complex whose diffeomorphism Ward identity agrees with the Bondi loss equations. It furthermore satisfies a trace relation due to Weyl invariance. Finally, I will show that the Carroll boosts are anomalous and that the anomaly is equal to one of the curvatures of the conformal Carroll algebra.

Carrollian derivation of the BMS flux-balance laws

I will present a derivation of the BMS evolution equations for the mass and angular momentum aspects in four-dimensional asymptotically flat space-time from purely boundary considerations. I will first give a general geometrical framework to implement gauge-fixing and asymptotic symmetries at the boundary and after recalling that the Bondi shear naturally sits within the Carrollian connection, I will argue that the boundary energy-momentum tensor has to be supplemented with hypermomenta of geometric origin, driving the non-conservation of the asymptotic charges. This constitutes the first step in establishing a holographic dictionary in asymptotically flat space-time, offering a geometric implementation of the radiative sources.

Superrotations at Spatial Infinity

The BMS (Bondi–van der Burg–Metzner–Sachs) group was shown long ago to be the group of asymptotic symmetries of gravity in asymptotically flat spacetime. This group naturally emerges at null infinity; however, analyses at spatial infinity did not exhibit any sign of the BMS group. This discrepancy was recently resolved by imposing appropriate “parity-twisted” boundary conditions at spatial infinity, leading to full agreement with the null-infinity result. Moreover, the BMS group admits an enlargement by extending the Lorentz algebra to the two‐dimensional conformal algebra into the so‐called superrotations. While superrotations have proven central at null infinity, they have remained elusive in spatial-infinity frameworks. In this talk, I will present a Hamiltonian (canonical) realization of superrotation symmetries at spatial infinity, thus providing the last missing piece in our understanding and characterization of the asymptotic structure of flat space at spatial infinity.

Towards a Flat Space Carrollian Hologram from AdS/CFT

Carrollian holography proposes that gravity in four-dimensional (4d) asymptotically flat spacetime is dual to a 3d Carrollian CFT living at null infinity. In this talk, I will explain how massless amplitudes in flat space can be re-expressed as Carrollian CFT correlators at the boundary, referred to as Carrollian amplitudes. I will show that these correlators naturally emerge from the Carrollian limit of holographic CFT correlators computed via AdS Witten diagrams, establishing a correspondence between the flat limit in the bulk and the Carrollian limit at the boundary. As a concrete application, I will implement the flat/Carrollian limit of the duality between 11d supergravity on AdS4xS7 and 3d N=8 ABJM theory, extracting supergravity amplitudes in flat space.

Log soft theorem, log translations, and asymptotic Einstein equations

The classical gravitational log soft theorem introduced by Laddha, Sahoo, and Sen exhibits a cancellation among terms, whose origin has remained elusive. I will show that such a cancellation follows from gauge invariance under logarithmic translations. If time permits, I will also discuss how the log soft theorem can be understood as a consequence of matching conditions for the gravitational field across timelike, null, and spatial infinity. Based on joint work with Gianni Boschetti and Guzmán Hernández-Chifflet.

On the mixed helicity sector of celestial symmetries

The mixed helicity sector of celestial symmetries has been largely unexplored so far. I will report on recent progress in expressing the mixed helicity charge bracket for gravity and YM theory in a closed form, revealing the key role played by the shadow transformation. The correspondence between the hard charge action on conformal primary fields and the celestial OPE provides consistency checks for, as well as new insights into, the inclusion of shadow operators in celestial CFT.

Universal sectors of Carrollian CFT_2

After revisiting modular invariance in Carrollian CFT_2 (CCFT_2), we show that there are regions of the modular parameters where the vacuum character dominates in the S-dual channel. We use this property to zoom into three different sectors of the CCFT_2, dubbed "Cardy", "Schwarzian", and "Boltzmann". We add a new entry in the Flat_3/CCFT_2 dictionary by providing a geometric interpretation of the Schwarzian sector of a (holographic) CCFT_2.