Past Relativity Seminar

In this talk, I will discuss my joint paper with Olivier Biquard and Paul Gauduchon on ALF Ricci-flat Riemannian  4-manifolds. My collaborators had previously classified all such spaces that are toric and Hermitian, but not Kaehler. Our main result uses an open curvature condition to prove a rigidity result of the following type: any Ricci-flat metric that is sufficiently close to a non-Kaehler, toric, Hermitian ALF solution (with respect to a norm that imposes reasonable fall-off at infinity) is actually  one of the  known Hermitian toric  solutions. 
 

I will present a pair of off-shell functionals in position space, localized on the self-dual and the anti-self-dual planes which naturally give the Parke-Taylor denominator. These can therefore be used: 
i) to compute scattering amplitudes of particles with different spins and helicities; and 
ii) develop a Lagrangian description. 
Using Witten's half-Fourier transform, I will express these functionals in twistor space and present the kernels in a closed compact form. For even multiplicities, I will show how to obtain this form geometrically which than then be “folded” to get the one-less odd-multiplicity result. 
 

I will review some recent developments in effective field theory of  composite higher-spin particles, namely, Zinoviev's massive gauge symmetry and 
the new chiral-field approach. The latter approach was inspired by a simple spinor-helicity structure first singled out by Arkani-Hamed, Huang and Huang, which encodes the higher-spin information of two massive particles. It turned out to be persistent in tree-level amplitudes with any number of additional identical-helicity gluons or gravitons, leading to the discovery of the chiral-field approach. I will mention the applications of massive higher-spin scattering amplitudes to classical gravitational dynamics of rotating black  holes. 
 

Explicit examples of the AdS/CFT correspondence where both bulk and boundary theories are tractable are hard to come by, but the minimal tension string on AdS_3 x S^3 x T^4  is one notable example. In this paper, we discuss how one can construct sigma models on twistor space, with a particular focus on applying these techniques to the aforementioned string theory. We derive novel incidence relations, which allow us to understand to what extent the minimal tension string encodes information about the bulk. We identify vertex operators in terms of bulk twistor variables and a map from twistor space to spacetime is presented. We also demonstrate the presence of a partially broken global supersymmetry algebra in the minimal tension string and we argue that this implies that there exists an N=2 formulation of the theory. The implications of this are studied and we demonstrate the presence of an additional constraint on physical states. This is based on work with Ron Reid-edwards https://arxiv.org/abs/2411.08836.

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. Utilizing the 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.

We present results (joint with Hiroshi isozaki, Matti lassas, and Teemu Tyni) on reconstruction of certain nonlinear wave operators from knowledge of their far field effect on incoming waves. The result depends on the reformulation of the problem as a non-linear Goursat problem in the Penrose conformal compactification, for suitably small incoming waves. The non-linearity is exploited to generate secondary waves, which eventually probe the geometry of the space-time. Some extensions to cosmological space-times will also be discussed.  Time permitting, we will contrast these results with near-field inverse scattering obtained for only linear waves, where no non-linearity can be exploited, and the methods depend instead on unique continuation. (The latter joint with Ali Feizmohammadi and Lauri Oksanen). 

The main challenges in constructing a holographic correspondence for asymptotically flat spacetimes lie in 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 demonstrate that there exists a systematic and mathematically robust approach to understanding and deriving the associated flux-balance laws from intrinsic boundary geometric considerations — an aspect of crucial importance for flat-space holography, as I shall argue during the presentation. 

For self-containment, I shall begin by reviewing key aspects of the geometry at null infinity, which has been termed conformal Carroll geometry. Reviving Ashtekar’s old statement, I shall emphasise that boundary affine connections possess degrees of freedom that precisely serve as the sources encoding radiation from a holographic perspective. I shall conclude by deriving flux-balance laws in an effective field theory framework at the boundary, employing novel techniques that introduce “hypermomenta” as responses to fluctuations in the boundary connection. The strength of our formalism lies in its ability to perform all computations in a manifestly coordinate- and Weyl-invariant manner within the framework of Sir Penrose’s conformal compactification.

Due to connections to flat space holography, Carrollian geometry, physics and fluid dynamics have received an explosion of interest over the last two decades. In the Carrollian limit of vanishing speed of light c, relativistic fluids reduce to a set of PDEs called the Carrollian fluid equations. Although in general these equations are not well understood, and their PDE theory does not appear to have been studied, in dimensions 1+1 it turns out that there is a duality with the Galilean compressible Euler equations in 1+1 dimensions inherited from the isomorphism of the Carrollian (c to 0) and Galilean (c to infinity) contractions of the Poincar\'e algebra. Under this duality time and space are interchanged, leading to different dynamics in evolution. I will discuss recent work with N. Athanasiou (Thessaloniki), M. Petropoulos (Paris) and S. Schulz (Pisa) in which we establish the first rigorous PDE results for these equations by introducing a notion of Carrollian isentropy and studying the equations using Lax’s method and compensated compactness. In particular, I will explain that there is global existence in rough norms but finite-time blow-up in smoother norms.

Galilean and Carrollian algebras are dual contractions of the Poincaré algebra. They act on two-dimensional Newton--Cartan and Carrollian manifolds and are isomorphic. A consequence of this property is a duality correspondence between one-dimensional Galilean and Carrollian fluids. I will describe the algebras and the dynamics of these systems as they emerge from the relevant  limits of Lorentzian hydrodynamics, and explore the advertised duality relationship. This interchanges longitudinal and transverse directions with respect to the flow velocity, and permutes equilibrium and out-of-equilibrium observables, unveiling specific features of Carrollian physics. I will also discuss the hydrodynamic-frame invariance in Lorentzian systems and its fate in the Galilean and Carrollian avatars.

In recent years, a novel approach to studying integrable models has emerged which leverages a higher-dimensional gauge theory, specifically a holomorphic-topological theory. This new framework provides alternative methods for investigating quantum aspects of integrability and for constructing integrable models in more than two dimensions. This talk will review the foundations of this approach, its applications, and the exciting possibilities it opens up for future research in the field of integrable systems. 

 I will first give a short review of the concepts of Asymptotically Flat Spacetimes, IR triangle and Noether's theorems. I will then present what Asymptotic Higher Spin Symmetries are and how they were introduced as a candidate for an approximate symmetry of General Relativity and the S-matrix. Next, I'll move on to the recent developments of establishing these symmetries as Noether symmetries and describing how they are canonically and non-linearly realized on the asymptotic gravitational phase space. I will discuss how the introduction of dual equations of motion encapsulates the non-perturbativity of the analysis. Finally I'll emphasize the relation to twistor, especially with 2407.04028. Based on 2409.12178 and 2410.15219

Physics beyond relativistic invariance and without Lorentz (or Poincaré) symmetry and the geometry underlying these non-Lorentzian structures have become very fashionable of late. This is primarily due to the discovery of uses of non-Lorentzian structures in various branches of physics, including condensed matter physics, classical and quantum gravity, fluid dynamics, cosmology, etc. In this talk, I will be talking about one such theory - Carrollian theory, where the Carroll group replaces the Poincare group as the symmetry group of interest. Interestingly, any null hypersurface is a Carroll manifold and the Killing vectors on the null manifold generate Carroll algebra. Historically, Carroll group was first obtained from the Poincaré group via a contraction by taking the speed of light going to zero limit as a “degenerate cousin of the Poincaré group”.  I will shed some light on Carrollian fermions, i.e. fermions defined on generic null surfaces. Due to the degenerate nature of the Carroll manifold, there exist two distinct Carroll Clifford algebras and, correspondingly, two different Carroll fermionic theories. I will discuss them in detail. Then, I will show some examples; when the dispersion relation becomes trivial, i.e. energy bands flatten out, there can be a possibility of the emergence of Carroll symmetry. 

We will explore the connection between Celestial and Euclidean Anti-de Sitter (EAdS) holography in the massive scalar case. Specifically, exploiting the so-called hyperbolic foliation of Minkowski space-time, we will show that each contribution to massive Celestial correlators can be reformulated as a linear combination of contributions to corresponding massive Witten correlators in EAdS. This result will be demonstrated explicitly both for contact diagrams and for the four-point particle exchange diagram, and it extends to all orders in perturbation theory by leveraging the bootstrapping properties of the Celestial CFT (CCFT).  Within this framework, the Kantorovic-Lebedev transform plays a central role. This transform will allow us to make broader considerations regarding non-perturbative properties of a CCFT.

Introduction to flat space holography in three dimensions and Carrollian CFT2, with selected results on correlation functions, thermal entropy, entanglement entropy and an outlook to Bondi news in 3d.

I will describe a holomorphic-topological field theory in eleven-dimensions which captures a 1/16-BPS subsector of eleven-dimensional supergravity. Remarkably, asymptotic symmetries of the theory on flat space and on twisted versions of the AdS_4 x S^7 and AdS_7 x S^4 backgrounds recover three of the five infinite dimensional exceptional simple super-Lie algebras. I will discuss some applications of this fact, including character formulae for indices counting multigravitons and the contours of a program to holographically describe 1/16-BPS local operators in the 6d (2,0) SCFTs of type A_{N-1}. This talk is based on joint work, much in progress, with Fabian Hahner, Ingmar Saberi, and Brian Williams.

In this talk I will explain how a dictionary between the Bondi-Sachs and the Newman-Penrose formalism can be used to organize the subleading data appearing in the metric for asymptotically-flat spacetimes. In particular, this can be used to show that the higher Bondi aspects can be traded for higher spin charges, and that the latter form a w_infinity algebra.

In recent years, the theme of asymptotically flat spacetimes has come back to the fore, fueled by the discovery of gravitational waves and the growing interest in what flat holography could be. In this quest, the standard tools pertaining to asymptotically anti-de Sitter spacetimes have been insufficiently exploited. I will show how Ricci-flat spacetimes are generally reached as a limit of Einstein geometries and how they are in fact constructed by means of data defined on the conformal Carrollian boundary that is null infinity. These data, infinite in number, are obtained as the coefficients of the Laurent expansion of the energy-momentum tensor in powers of the cosmological constant. This approach puts this tensor back at the heart of the analysis, and at the same time reveals the versatile role of the boundary Cotton tensor. Both appear in the infinite hierarchy of flux-balance equations governing the gravitational dynamics.  

This will be an informal discussion seminar based on https://arxiv.org/abs/2211.07592:

The constrained Hamiltonian analysis of geometric actions is worked out before applying the construction to the extended Bondi-Metzner-Sachs group in four dimensions. For any Hamiltonian associated with an extended BMS4 generator, this action provides a field theory in two plus one spacetime dimensions whose Poisson bracket algebra of Noether charges realizes the extended BMS4 Lie algebra. The Poisson structure of the model includes the classical version of the operator product expansions that have appeared in the context of celestial holography. Furthermore, the model reproduces the evolution equations of non-radiative asymptotically flat spacetimes at null infinity.

We present a new formulation of string and particle amplitudes that emerges from simple one-dimensional models. The key is a new way to parametrize the positive part of Teichmüller space. It also builds on the results of Mirzakhani for computing Weil-Petterson volumes. The formulation works at all orders in the perturbation series, including non-planar contributions. The relationship between strings and particles is made manifest as a "tropical limit". The results are well adapted to studying the scattering of large numbers of particles or amplitudes at high loop order. The talk will in part cover results from arXiv:2309.15913, 2311.09284.

Recently, the Newman-Janis shift has been revisited from the angle of scattering amplitudes in terms of the so-called "massive spinor-helicity variables," tracing back to Penrose and Perjés in the 70s. However, well-established results are limited in the same-helicity (self-dual) sector, while a puzzle of spurious poles arises in mixed-helicity sectors. This talk will outline how massive twistor theory can reproduce the same-helicity results while offering a possible solution to the spurious pole puzzle. Firstly, the Newman-Janis shift in the same-helicity sector is derived from a complexified version of the equivalence principle. Secondly, the massive twistor particle is coupled to background fields from bottom-up and top-down perspectives. The former is based on perturbations of symplectic structures in massive twistor space. The latter provides a generalization of Newman-Janis shift in generic backgrounds, which also leads to "curved massive twistor space" and its deformed massive incidence relation. Lastly, the Feynman rules of the first-quantized massive twistor particle and their physical interpretation are briefly discussed. Overall, a significant emphasis is put on the Kähler geometry ("zig-z̄ag structure") of massive twistor space, which eventually connects to a worldsheet structure of the Kerr solution.

I will show that the massless irreducible representations of the Poincare group are precisely Corrolian field living on I^+. I will also show that the analogous massless irreducible representation of E11 are just the degrees of freedom of maximal supergravity. Finally I will speculate how spacetime could emerge from an underlying fundamental theory.

The Celestial Holography program encompasses recent efforts to understand the flat space hologram in terms of a CFT living on the celestial sphere. Here we have fun relating various extrapolate dictionaries in CCFT and examining tools we can apply when perturbing around a 4D CFT in the bulk.

Hydrodynamics allow for efficient computation of many-body dynamics and have been successfully used in the study of black hole horizons, collective behaviour of QCD matter in heavy ion collisions, and non-equilibrium behaviour in strongly-interacting condensed matter systems.
In this talk, I will present the application of hydrodynamics to quantum field theory with an infinite number of local conservation laws. Such an integrable system can be described within the recently developed framework of generalised hydrodynamics. I will present the key assumptions of generalised hydrodynamics as well as summarise some recent developments in this field. In particular, I will concentrate on the study of the SU(3)_2-Homogeneous sine-Gordon model. Thanks to the hydrodynamic approach, we were able to identify the key dynamical signatures of unstable excitations in this integrable quantum field theory and simulate the real time RG-flow of the theory between interacting and free conformal regimes.
The talk is based on joint work with Olalla Castro-Alvaredo, Cecilia De Fazio and Benjamin Doyon.

In this talk I will review some of the key ideas behind the study of entanglement measures in 1+1D quantum field theories employing the so-called branch point twist field approach. This method is based on the existence of a one-to-one correspondence between different entanglement measures and different multi-point functions of a particular type of symmetry field. It is then possible to employ standard methods for the evaluation of correlation functions to understand properties of entanglement in bipartite systems. Time permitting, I will then present a recent application of this approach to the study of a new entanglement measure: the symmetry resolved entanglement entropy.

Black hole horizons are normally at finite spatial distance from the exterior region, but when they are degenerate (or extreme as they are usually referred to in this case) the spatial distance becomes infinite. One can still fall into the black hole in finite proper time but the crossing sphere is replaced by an "internal infinity". Near to the horizon of an extreme Kerr black hole, the scattering properties of test fields bear some similarities to what happens at an asymptotically flat infinity. This observation triggered a natural question concerning the peeling behaviour of test fields near such horizons. A geometrical tool known as the Couch-Torrence inversion is particularly well suited to studying this question. In this talk, I shall recall some essential notions on the peeling of fields at an asymptotically flat infinity and describe the Couch-Torrence inversion in the particular case of extreme Reissner-Nordström black holes, where it acts as a global conformal isometry of the spacetime. I will then show how to extend this inversion to more general spherically symmetric extreme horizons and describe what results can be obtained in terms of peeling. This is a joint ongoing project with Jack Borthwick (University of Besançon) and Eric Gourgoulhon (Paris Observatory).

Holography in asymptotically flat spaces is one of the most coveted goals of modern mathematical physics. In this talk, I will motivate a novel holographic description of self-dual SO(8) Yang-Mills + self-dual conformal gravity on a Euclidean signature, asymptotically flat background called Burns space. The holographic dual lives on a stack of D1-branes wrapping a CP^1 cycle in the twistor space of R^4 and is given by a gauged beta-gamma system with SO(8) flavor and a pair of defects at the north and south poles. It provides the first example of a stringy realization of (asymptotically) flat holography and is a Euclidean signature variant of celestial holography. This is based on ongoing work with Kevin Costello and Natalie Paquette.

A particle physics approach to describing black hole interactions is opening new avenues for understanding gravitational-wave observations. We will start by reviewing this paradigm change, showing how to compute observables in general relativity from amplitudes on flat spacetime. We will then present a generalization of this framework for amplitudes on curved backgrounds. Evaluating the required one-to-one amplitudes already shows remarkable structures. We will discuss them in detail, including eikonal behaviours and unexpected KLT-like factorization properties for amplitudes on stationary backgrounds. We will then conclude by discussing applications of these amplitudes to strong field observables such as the impulse on a curved background and memory effects

Non-shearing congruences of null geodesics on four-dimensional Lorentzian manifolds are fundamental objects of mathematical relativity. Their prominence in exact solutions to the Einstein field equations is supported by major results such as the Robinson, Goldberg-Sachs and Kerr theorems. Conceptually, they lie at the crossroad between Lorentzian conformal geometry and Cauchy-Riemann geometry, and are one of the original ingredients of twistor theory.
 
Identified as involutive totally null complex distributions of maximal rank, such congruences generalise to any even dimensions, under the name of Robinson structures. Nurowski and Trautman aptly described them as Lorentzian analogues of Hermitian structures. In this talk, I will give a survey of old and new results in the field.

In the first part of this talk, we will (briefly) derive the original calculation by Hawking in 1974 to determine the radiation given off by a black hole, giving the result in the form of an integral of a classical solution to the linear wave equation.
In the second part of the talk, we will take this integral as a starting point, and rigorously calculate the radiation given off by a forming spherically symmetric, charged black hole. We will then show that for late times in its formation, the radiation given off approaches the limit predicted by Hawking, including the extremal case. We will also calculate a bound on the rate at which this limit is approached.

I'll argue that the celestial holography program looks a lot like the twisted holography program when studied on twistor space.  The chiral algebras in celestial holography can be seen by applying techniques such as Koszul duality to holomorphic theories on twistor space. Along the way, I will discuss the role of one-loop gauge anomalies on twistor space and when they can be cancelled by a Green-Schwarz mechanism.   This is joint work in progress with Natalie Paquette.

The speaker will be on zoom, but for a more interactive experience, some of the audience will watch the seminar in L5.

The recent progress of applying QFT methods to classical GR has provided a new perspective on the Kerr black hole solution. Its leading gravitational interactions are known to involve an infinite tower of spin-induced multipoles with unit coupling constants. In this talk, I will present a novel form of the classical worldline action that implements these multipole interactions within a single worldsheet integral, which is inspired by the Newman-Janis shift relationship of the Kerr and Schwarzschild solutions. I will also discuss connections to our recently discovered ability to model such interactions using a certain family of scattering amplitudes, as well as a simple double-copy property hidden within. 

This will be an in-person seminar run in hybrid mode.

Penrose's proposal of smooth conformal compactification is not only of geometric elegance, it also makes concrete predictions on physically measurable objects such as the "late-time tails" of gravitational waves.  At the same time, the physical motivation for a smooth null infinity remains itself unclear. In this talk, building on arguments due to Christodoulou, Damour and others, I will show that, in generic gravitational collapse, the "peeling property" of gravitational radiation is violated (so one cannot attach a smooth null infinity). Moreover, I will explain how this violation of peeling is in principle measurable in the form of leading-order deviations from the usual late-time tails of gravitational radiation.

This talk is based on https://arxiv.org/abs/2105.08079, https://arxiv.org/abs/2105.08084 and … .

It will be a hybrid seminar on both zoom and in-person in L5. 

We will present the precise late-time asymptotics for scalar fields on both extremal and sub-extremal black holes including the full Reissner-Nordstrom family and the subextremal Kerr family. Asymptotics for higher angular modes will be presented for all cases. Applications in observational signatures will also be discussed. This work is joint with Y. Angelopoulos (Caltech) and D. Gajic (Cambridge)

I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

Plebanski generating functions give a compact encoding of the geometry of self-dual Ricci-flat space-times or hyper-Kahler spaces.  They have applications as generating functions for BPS/DT/Gromov-Witten invariants.  We first show that Plebanski's first fundamental form also provides a generating function for the gravitational MHV amplitude.  We then obtain these Plebanski generating functions from the corresponding twistor spaces as the value of the action of new sigma models for holomorphic curves in twistor space.   
In four-dimensions, perturbations of the hyperk¨ahler structure corresponding to positive helicity gravitons. The sigma model’s perturbation theory gives rise to a sum of tree diagrams for the gravity MHV amplitude observed previously in the literature, and their summation via a matrix tree theorem gives a first-principles derivation of Hodges’ determinant formula directly from general relativity. We generalise the twistor sigma model to higher-degree (defined in the first instance with a cosmological constant), giving a new generating principle for the full tree-level graviton S-matrix in general with or without  cosmological constant.  This is joint work with Tim Adamo and Atul Sharma in https://arxiv.org/abs/2103.16984.  

The outstanding issue of a non-singular extension of the Kerr-NUT- (anti) de Sitter solutions to Einstein’s equations is solved completely. The Misner’s method of obtaining the extension for Taub-NUT spacetime is generalized in a non-singular manner. The Killing vectors that define non-singular spaces of non-null orbits are derived and applied. The global structure of spacetime is discussed. The non-singular conformal geometry of theinfinities is derived. The Killing horizons are present.

The propagation of high-frequency electromagnetic waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and polarization-dependent corrections at first order in wavelength modify the propagation of light in an inhomogenous medium via a spin-orbit coupling mechanism. This effect, known as the spin Hall effect of light, has been experimentally observed. In this talk I will discuss recent work which generalizes the spin Hall effect to the propagation of light and gravitational waves in inhomogenous spacetimes. This is based on joint work with Marius Oancea and Jeremie Joudioux.

I will connect approaches to classical integrable systems via 4d Chern-Simons theory and via symmetry reductions of the anti-self-dual Yang-Mills equations. In particular, I will consider holomorphic Chern-Simons theory on twistor space, defined using a range of meromorphic (3,0)-forms. On shell these are, in most cases, found to agree with actions for anti-self-dual Yang-Mills theory on space-time. Under symmetry reduction, these space-time actions yield actions for 2d integrable systems. On the other hand, performing the symmetry reduction directly on twistor space reduces the holomorphic Chern-Simons action to 4d Chern-Simons theory.