Past Relativity Seminar

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.