Yannick Herfray

A bstract: The infrared structure of QED and gravity is known to be governed by an infinite-dimensional symmetry group which extends the Poincaré group to include, respectively, large U(1) transformations and BMS supertranslations. We describe how the unitary irreducible representations (UIRs) of these asymptotic symmetry groups encode universal infrared features of a scattering process. Motivated by the goal of defining an infrared-finite S -matrix based on these UIRs, we also study supermomentum eigenstates and contrast our construction with the dressed-state approach for infrared-safe amplitudes.

Des Twisteurs de Penrose aux Trois-Formes de Hitchin : nouvelles Perspectives sur la Gravité d'Einstein: Dans cette thèse nous explorons les aspects de la gravité d'Einstein qui sont propres à la dimension quatre.L'une des propriétés surprenantes liées à cette dimension est la possibilité de formuler la gravité de manière 'Chirale'. Dans ce type de reformulations, typiquement, la métrique perd son rôle centrale. La correspondance entre espace-temps et espace des twisteurs est un autre aspect propre à la dimension quatre. Ces formulations, Chirale et Twistorielle, semblent très différentes. Dans la première partie de cette thèse nous montrons qu'elles sont en fait intimement liées: en particulier nous proposons une nouvelle preuve du `théorème du graviton non-linéaire', due à Penrose, dont le cœur est la géométrie des SU(2)-connections (plutôt qu'une métrique). Dans la seconde partie de cette thèse nous montrons que la gravité en trois et quatre dimensions est liée à des théories d'une nature complètement différentes en dimension six et sept. Ces théories, due à Hitchin, sont des théories de trois-formes différentielles invariantes sous difféomorphismes. En dimensions sept, nous rencontrons seulement un succès partiel puisque la théorie 4D qui en résulte est une version modifiée de la gravité. Cependant nous prouvons au passage que les solutions d'une déformation particulière de la gravité ont, en 7D, l’interprétation de variétés avec holonomies G2.Par contre, en réduisant la théorie de six à trois dimensions nous obtenons précisément la gravité 3D. Nous présentons aussi de nouvelles fonctionnelles pour les formes différentielles en six dimensions. Toutes sont invariantes sous difféomorphismes et deux d’entre elles sont topologiques.

In these lecture notes, a group-theoretical introduction to BMS symmetries is provided in a self-contained manner. More precisely, all definitions and structures are purely based on geometrical and group-theoretical notions defined at null infinity and valid in any dimension, in a way that circumvents its traditional bulk realisation as asymptotic symmetries. The topics which are reviewed are: the definition of BMS transformations as conformal Carrollian isometries of null infinity, the semidirect structure of the BMS group, the holographic reconstruction of Minkowski spacetime in terms of good cuts, the one-to-one correspondence between good cut subspaces and Poincaré subgroups (aka vacua), as well as a basic introduction to unitary representations of the BMS group.

The goal of this paper is to provide a definition for a notion of extended boundary at time and space-like infinity which, following Figueroa-O'Farril--Have--Prohazka--Salzer, we refer to as Ti and Spi. This definition applies to asymptotically flat spacetime in the sense of Ashtekar--Romano and we wish to demonstrate, by example, its pertinence in a number of situations. The definition is invariant, is constructed solely from the asymptotic data of the metric and is such that automorphisms of the extended boundaries are canonically identified with asymptotic symmetries. Furthermore, scattering data for massive fields are realised as functions on Ti and a geometric identification of cuts of Ti with points of Minkowksi then produces an integral formula of Kirchhoff type. Finally, Ti and Spi are both naturally equipped with (strong) Carrollian geometries which, under mild assumptions, enable to reduce the symmetry group down to the BMS group, or to Poincaré in the flat case. In particular, Strominger's matching conditions are naturally realised by restricting to Carrollian geometries compatible with a discrete symmetry of Spi.

We construct wave functions for unitary irreducible representations (UIRs) of the Bondi-Metzner-Sachs (BMS) group, i.e., BMS particles, and show that they describe 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 nonlinear, decomposition of supermomenta into hard and soft pieces.

We revisit the classification, and give explicit realisations, of unitary irreducible representations of the BMS group. As compared to McCarthy's seminal work, we make use of a unique, Lorentz-invariant, decomposition of supermomenta into a hard and a soft piece, that we introduce and properly define, to investigate the extent to which generic representations depart from usual Poincaré particles and highlight their relations to gravitational infrared physics. We insist on making wavefunctions as explicit as possible. Similarly, we explain how branching to a Poincaré subgroup works in practice: this is physically relevant because this amounts to reading off the field content of a given BMS state in terms of a choice of gravity vacuum. In particular, we emphasise how different gravity vacua differ in their interpretation of the same BMS state, here again providing concrete examples as well as the general procedure. Finally, we demonstrate on an example that generic BMS particles are flexible enough to encode memory, as opposed to usual Poincaré particles.

We construct an explicit realization of the action of the \mathscr Lw_{1+∞} ℒ w 1 + ∞ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of \mathscr Lw_{1+∞} ℒ w 1 + ∞ symmetries in twistor space, ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of \mathscr Lw_{1+∞} ℒ w 1 + ∞ Noether charges on the asymptotic phase space.