Abstracts
Tim Adamo
Title: The first celestial holographer
Abstract: Ezra 'Ted' Newman is widely known as a hero of the Golden Age of General Relativity, with many fundamental constructions in GR carrying his name. Four years on from his death, Ted's ideas remain an important source of inspiration for many of us. After a brief history of the most famous works by Newman and his collaborators, I will focus on a set of his ideas which are, perhaps, less widely known. A large portion of Newman's career was devoted to exploring the question: How much of an asymptotically flat spacetime can be constructed from its data at null infinity? With the benefit of hindsight, this can be viewed as an early attempt at something like bulk reconstruction for asymptotically flat spacetimes. I will demonstrate how Newman's work on this topic underpins various aspects of celestial holography, and suggests many avenues for future exploration.
Bernardo Araneda
Title: Complex geometry and gravitational instantons
Abstract: The heavenly and twistor programmes of Newman and Penrose uncovered deep links between complex geometry and gravitation, leading in particular to the discovery of complex structures in black holes. These structures are more naturally understood in Euclidean signature, where the corresponding solutions are called gravitational instantons and play a central role in Euclidean quantum gravity. In Euclidean signature, the black hole uniqueness conjecture is false, due to the recent discovery of the remarkable Chen-Teo instanton. It was subsequently proved that this solution also has a complex structure, suggesting deeper connections between complex geometry and instantons. In this talk, we shall show that generic infinitesimal deformations of ALF gravitational instantons have complex structures. This allows us to prove the conjecture that the Moduli Space is a smooth manifold near Hermitian points. This is joint work with Lars Andersson.
Lydia Bieri
Title: Asymptotics of Radiative Spacetimes
Abstract: In this talk, we shall discuss solutions of the Einstein equations for various physical scenarios. In particular, we will highlight structures at null infinity of asymptotically-flat spacetimes and extract information about gravitational radiation and memory. Questions around peeling, as well as antipodal symmetry and non-symmetry problems will be addressed along the way.
Roland Bittleston
Title: Quantum Fields on Twistor Space
Abstract: In these lectures I will introduce quantum field theory on twistor space, with gauge theory as the motivating example. I will begin by reviewing the Penrose-Ward transformation and how it can be used to recast the self-dual sector of gauge theory as a holomorphic field theory on twistor space. This holomorphic theory is sick at one-loop: it suffers from a gauge anomaly. Cancelling the anomaly yields a quantum integrable theory on space-time. I will then elucidate the Costello-Paquette correspondence, which leverages this integrability to compute gauge theory amplitudes and form factors using chiral algebra techniques. Time permitting, I will explain how many of these ideas extend to self-dual gravity.
Jordan Cotler
Title: Carrollian Holography and Non-locality
Abstract: We explore whether it is possible to construct a local Carrollian CFT dual to flat space Einstein quantum gravity. Beginning with the quantization of Carrollian field theories, we argue that perturbative renormalization forces the theory to degenerate into either a generalized free field or a purely classical system in which all loop corrections vanish. This behavior reflects the divergence of the effective central charge when a UV cutoff is introduced. Although one may remove this divergence by e.g. taking a non-Lagrangian limit of certain Carrollian CFTs, doing so breaks conformal invariance. Together with complementary consistency arguments, our results indicate that any Carrollian CFT dual to flat-space quantum gravity must be intrinsically nonlocal.
Maciej Dunajski
Title: Quasi—local mass, the Penrose property of Scri, and causality.
Abstract: I will discuss two approaches to mass in General Relativity. One quasi—local, and applicable to closed surfaces in space times (like that of the Kerr horizon), and one global, based on causal properties of Scri. In the second approach, the causal properties of asymptotically flat spacetimes depend on their dimensionality: while the time-like future of any point in the past conformal infinity contains the whole of the future conformal infinity in 2+1 and 3+1 dimensional Schwarzschild spacetimes, this property does not hold for (d + 1) dimensional Schwarzschild if d > 3.
Laurent Freidel
Title: Higher spin symmetry in Gravity and Yang-Mills and Newman's good cuts
In this talk I'll review the construction from phase space of a tower of asymptotic charges that includes the mass aspect, the angular momentum aspect and a tower of similar higher spin charges. I will show that they generates a canonical algebra which provides a non linear generalization of LW_{\infty} when the shear doesn’t not vanish. I will also present how this construction provides a new perspective on the connection between asymptotic infinity and twistor theory. I will highlight how ideas from Ted Newman about the good cuts gives a fresh perspective on the construction of gauge invariant observables and the relationship between asymptotic symmetries and twistors.
Adam Kmec
Title: Twistor Charges for the S-algebra
Abstract: In this talk, we will discuss how twistor theory can help understand the S-algebra, which arises as the reinterpretation of collinear limits of the Yang-Mills S-matrix as OPEs in celestial holography. We work in the self-dual sector with the associated twistor action that describes the self-dual background and an anti-self-dual perturbation. Using covariant phase space methods, we construct two infinite towers of Hamiltonian charges arising from the symmetries of the action. The constructed charges can be shown to satisfy the expected algebra, including the S-algebra. Using twistor integral formula, we can translate the charges to null infinity, where they generate non-local variations of the asymptotic data, preserving the equations of motion. Furthermore, by considering the charges living on spatial infinity, we find the vertex algebras considered in twisted holography. This talk is based on joint work with Lionel Mason, Atul Sharma, and Romain Ruzziconi.
Silvia Nagy
Title: Sub^n-leading asymptotics in YM and gravity
Abstract: It is by now well understood how leading soft theorems follow as Ward identities of asymptotic symmetries defined at null infinity. For subleading infrared effects, the connection is more subtle, but it turns out that this can be formalised, to all orders in the energy expansion, by adapting the Stuckelberg procedure to construct an extended radiative phase space at null infinity. I will exemplify this with Yang-Mills theory and some work in progress in gravity, showing the construction of the extended phase space, as well as the charges corresponding to the subleading soft theorems at all orders. These turn out to satisfy simple recursion relations and organise themselves into infinite dimensional algebras. Time permitting, I will also review homotopy algebras, and show how they can, in the context of flat space holography, precisely encode the projection of fields to null infinity.
Roger Penrose
Title: Bi-twistor theory: replacing alpha planes by null geodesics
Bi-twistor theory is a natural extension of twistor theory in which a bi-twistor is a direct sum of a twistor and a duel twistor. They have a natural skew triple product coming from quantum mechanics. At the classical level, we can incorporate the theory into curved space-times where the basic equation is a weak form of the twistor equation. This leads us to a 4-complex-dimensional algebra in which there is a scalar product providing a norm which vanishes along null geodesics. These reflect the role of alpha planes in the non-linear graviton construction, but unlike the latter null geodesics are ubiquitous in general space-times.
Andrea Puhm
Title: Infrared surprises in gravity and celestial CFT
Abstract: The ``infrared triangle'' is an abstraction that encapsulates universal features of gravitational scattering in the infrared in the form of soft theorems and memory effects which can be traced to an underlying asymptotic symmetry. The long-range nature of gravitational interactions crucially modifies these infrared relations through novel soft theorems with logarithmic dependence on the energy together with late-time tails in the gravitational field that give rise to so-called tail memory effects. I will show that these long-range effects give rise to novel conservation laws in gravity and gauge theory and establish complete classical infrared triangles. By virtue of being universal and exact to all orders in the coupling, this is a key element for a holographic principle in spacetimes with flat asymptotics.
Atul Sharma
Title: Advances in Flat Holography
Abstract: These lectures will discuss applications of twistor theory to celestial holography. We will review topological strings and branes and use them to construct holographic duals of certain local holomorphic theories in twistor space. By the Penrose transform, local holomorphic theories on twistor space give rise to integrable theories on spacetime. Their celestial duals arise as 2d chiral CFTs living on D-branes. With pedagogical examples, we will show that 2d CFT correlators reproduce scattering amplitudes in the bulk.
David Skinner
Title: A Top-Down Construction of Self-Dual Einstein Gravity
Abstract: To date, top-down constructions of celestial holography involve a combination of twisted holography and twistor theory. In the original (Burns) model of Costello-Paquette-Sharma the bulk theory is the B model living in a suitable twistor space, corresponding to a theory of self-dual conformal gravity in four dimensions. I'll discuss a variant which comes from the B-model on a CY 5-fold admitting a K3 fibration over twistor space. This yields self-dual Einstein gravity in four dimensions.
Evgeny Skvortsov
Title: M-theory of all self-dual ones: AdS/CFT, stringy and celestial holography
Abstract: I will give a brief overview of the quest to construct quantum gravity models via higher-spin gravities. The most promising candidate—chiral higher-spin gravity—can be understood as an 'M-theory' for all self-dual theories. In particular, it is expected to admit a natural formulation in twistor space, as is already the case for some of its truncations. Chiral higher-spin gravity is related via the AdS/CFT correspondence to (Chern-Simons) vector models and can explain the remarkable 3D bosonization duality. It also implies the existence of new 'self-dual' conformal field theories on the boundary. Along similar lines, there is a potential connection to tensionless strings in AdS(4) and the ABJ theory. Finally, I will cover recent developments in celestial holography that are connected to chiral higher-spin gravity.
Andrew Strominger
Title: Soft Algebras in AdS4, dS4 and Newman Holography
Robert Wald
Title: Memory, Infrared Entanglement, and the Idealization of Scattering from Infinity
Abstract: 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.