Past Relativity Seminar

Spacetimes with compact directions play an important role in supergravity and string theory. The simplest such example is the Kaluza-Klein spacetime, where the compact space is a flat torus. An interesting question to ask is whether this spacetime, when viewed as an initial value problem, is stable to small perturbations of initial data. In this talk I will discuss the global, non-linear stability of the Kaluza-Klein spacetime to toroidal-independent perturbations and the particular nonlinear structure appearing in the associated PDE system.

Precision predictions for binary mergers are essential for the nascent field of gravitational wave astronomy. The initial inspiral part can be treated perturbatively. We present results for the post-Minkowskian expansion of conservative binary dynamics, previously available only at the 2nd order for several decades, at the 3rd and 4th orders in the expansion. Our calculations are based on quantum field theory and use powerful methods developed in the modern scattering amplitudes program, as well as loop integration techniques developed for precision collider physics. Furthermore, we take initial steps in calculating radiative binary dynamics and obtain analytically the total radiated energy in hyperbolic black hole scattering, at the lowest order in G but all orders in velocity.

Motivated by an attempt to construct a theory of quantum gravity as a perturbation around some flat background, Penrose has shown that, despite being asymptotically flat, there is an inconsistency between the causal structure at infinity of Schwarzschild and Minkowski spacetimes. This suggests that such a perturbative approach cannot possibly work. However, the proof of this inconsistency is specific to 4 spacetime dimensions. In this talk I will discuss how this result extends to higher (and lower) dimensions. More generally, I will consider examples of how the causal structure of asymptotically flat spacetimes are affected by dimension and by the presence of mass (both positive and negative). I will then show how these ideas can be used to prove a higher dimensional extension of the positive mass theorem of Penrose, Sorkin and Woolgar.

After a review of Batalin-Vilkovisky formalism and homotopy algebras, we discuss how these structures emerge in quantum field theory and gravity. We focus then on the application of these sophisticated mathematical tools to scattering amplitudes (both tree- and loop-level) and to the understanding of the dualities between gauge theories and gravity, highlighting generalizations of old results and presenting new ones.

We construct a class of Cauchy initial data without (marginally) trapped surfaces whose future evolution is a trapped region bounded by an apparent horizon, i.e., a smooth hypersurface foliated by MOTS. The estimates obtained in the evolution lead to the following conditional statement: if Kerr Stability holds, then this kind of initial data yields a class of scale critical vacuum examples of Weak Cosmic Censorship and the Final State Conjecture. Moreover, owing to estimates for the ADM mass of the data and the area of the MOTS, the construction gives a fully dynamical vacuum setting in which to study the Spacetime Penrose Inequality. We show that the inequality is satisfied for an open region in the Cauchy development of this kind of initial data, which itself is controllable by the initial data. This is joint work with Nikos Athanasiou https://arxiv.org/abs/2009.03704.

Since the seminal work of Penrose, it has been understood that conformal compactifications (or "asymptotic simplicity") is the geometrical framework underlying Bondi-Sachs' description of asymptotically flat space-times as an asymptotic expansion. From this point of view the asymptotic boundary, a.k.a "null-infinity", naturally is a conformal null (i.e degenerate) manifold. In particular, "Weyl rescaling" of null-infinity should be understood as gauge transformations. As far as gravitational waves are concerned, it has been well advertised by Ashtekar that if one works with a fixed representative for the conformal metric, gravitational radiations can be neatly parametrized as a choice of "equivalence class of metric-compatible connections". This nice intrinsic description however amounts to working in a fixed gauge and, what is more, the presence of equivalence class tend to make this point of view tedious to work with.

I will review these well-known facts and show how modern methods in conformal geometry (namely tractor calculus) can be adapted to the degenerate conformal geometry of null-infinity to encode the presence of gravitational waves in a completely geometrical (gauge invariant) way: Ashtekar's (equivalence class of) connections are proved to be in 1-1 correspondence with choices of (genuine) tractor connection, gravitational radiation is invariantly described by the tractor curvature and the degeneracy of gravity vacua correspond to the degeneracy of flat tractor connections. The whole construction is fully geometrical and manifestly conformally invariant.

In this talk I will present some recent explorations of cluster-algebraic patterns in the building blocks of scattering amplitudes in N = 4 super Yang-Mills theory. In particular, I will first briefly introduce the main characters on stage, i.e. Leading Singularities, Landau singularities, the amplituhedron and cluster algebras. I will then present my main conjecture, "LL-adjacency", which makes all the above characters play together: given a maximal cut of a loop amplitude, Landau singularities and poles of each Yangian invariant appearing in any representation of the corresponding Leading Singularities can be found together in a cluster.  I will explain how the conjecture has been tested for all one-loop amplitudes up to 9 points using cluster algebraic and amplituhedron-based methods.  Finally, I will discuss implications for computing loop amplitudes and their singularity structure, and open research directions.

This is based on the joint work with Ömer Gürdoğan (arXiv: 2005.07154).

Ambitwistor strings are a class of holomorphic worldsheet models that directly describe massless quantum field theories, such as supergravity and super Yang-Mills. Their correlators give remarkably compact amplitude representations, known as the CHY formulas: characteristic worldsheet integrals that are fully localized on a set of polynomial constraints known as the scattering equations. Moreover, the ambitwistor string models provide a natural way of extending these formulas to loop level, where the constraints can be used to simplify the formulas (originally on higher genus curves) to 'forward limit-like' constructions on nodal spheres. After reviewing these developments, I will discuss one of the peculiar features of this approach: the worldsheet formulas on nodal spheres result in a non-standard integrand representation that makes it difficult to e.g. apply established integration techniques. While several approaches for addressing this look feasible or have been put forward in the literature, they only work for the simplest toy models. Taking inspiration from these attempts, I want to discuss a novel strategy to overcome this difficulty, and formulate compact worldsheet formulas with standard Feynman propagators.

A motivation in the development of string theory was the 'duality' flip, exchanging the s- and t-channels, which relates all the cubic Feynman graphs at each order in perturbation theory, with fixed planar structure. In string theory, we can understand this as coming from the moduli spaces of marked surfaces, with the cubic diagrams corresponding to complete triangulations. I will describe how geometric-type cluster algebras give a surprising 'linear' way to talk about the same combinatorial problem, using results from work with N Arkani-Hamed and H Thomas and G Salvatori. This gives new ways to compute cubic scalar amplitudes, and new families of integrals generalizing the Veneziano amplitude.

The asymptotically locally Euclidean Ricci-flat self-dual 4-manifolds were classified and constructed by Kronheimer as hyperkahler quotients. Each belongs to a finite-dimensional family and a particularly interesting subfamily consists of manifolds with a circle action which can be identified with the minimal resolution of a quotient singularity C^2/G where G is a finite subgroup of SU(2). The resolved singularity is a configuration of rational curves and there is a distinguished one which is pointwise fixed by the circle action. The talk will give an explicit description of the induced metric on this central sphere, and involves twistor theory and the geometry of the lines on a cubic surface.
 

A well-known theorem of Choquet-Bruhat and Geroch states that for given smooth initial data for the Einstein equations there exists a unique maximal globally hyperbolic development. In particular, time evolution of globally hyperbolic solutions is unique. This talk investigates whether the same result holds for quasilinear wave equations defined on a fixed background. After recalling the notion of global hyperbolicity, we first present an example of a quasilinear wave equation for which unique time evolution in fact fails and contrast this with the Einstein equations. We then proceed by presenting conditions on quasilinear wave equations which ensure uniqueness. This talk is based on joint work with Harvey Reall and Felicity Eperon.
 

 I will give an overview of my recent research on the definition of asymptotic charges in asymptotically flat spacetimes, including the definition of subleading and dual BMS charges and the relation to the conserved Newman-Penrose charges at null infinity.

A polynomial form is established for the off-shell CHY scattering equations proposed by Lam and Yao. Re-expressing this in terms of independent Mandelstam invariants provides a new expression for the polynomial scattering equations, immediately valid off shell, which makes it evident that they yield the off-shell amplitudes given by massless ϕ3 Feynman graphs. A CHY expression for individual Feynman graphs, valid even off shell, is established through a recurrence relation.

This talk will explain how Lie polynomials underpin the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides).  ABHY have recently shown that Lie polynomials arise naturally also in the geometry of the space K_n of momentum invariants, Mandelstams, and can be expressed in the space of n-3-forms dual to certain associahedral (n-3)-planes. They also arise in the moduli space M_{0,n} of n points on a Riemann sphere up to Mobius transformations in the n-3-dimensional homology.  The talk goes on to give a natural correspondendence between K_n and the cotangent bundle of M_{0.n} through which the relationships of some of these structures can be expressed.  This in particular gives a natural framework for expressing the CHY and ambitwistor-string formulae for scattering amplitudes of gauge and gravity theories and goes some way to expressing their double copy relations.   This is part of joint work in progress with Hadleigh Frost.

Feynman integrals govern the perturbative expansion in quantum field theories. As periods, these integrals generate representations of a motivic Galois group. I will explain this idea and illustrate the 'coaction principle', a mechanism that constrains which periods can appear at any loop order.
 

In this talk, I will describe new mathematical structures in the low-energy  expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited  to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic  Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string  low-energy expansions.
 

 It has been long known that intersection theory on the moduli space of punctured Riemann surfaces encodes observables in two-dimensional quantum gravity. It is natural to ask whether interacting theories could also admit a similar description. In the genus-zero case we put forward a twisted version of intersection theory on the moduli space and propose that it computes tree-level scattering amplitudes in a range of quantum field theories with a finite spectrum of particles. The resulting intersection numbers exhibit two alternative kinds of localization formulae. The first one receives contributions only from boundaries of the moduli space, thus leading to a Feynman diagram expansion, while the second one localizes on critical points of a certain Morse function.

In the speaker's previous joint work with Hans-Joachim Hein, a mass formula for asymptotically locally Euclidean (ALE) Kaehler manifolds was proved, assuming only relatively weak fall-off conditions on the metric. However, the case of real dimension four presented technical difficulties that led us to require fall-off conditions in this special dimension that are stronger than the Chrusciel fall-off conditions that sufficed in higher dimensions. This talk will explain how a new proof of the 4-dimensional case, using ideas from symplectic geometry, shows that Chrusciel fall-off suffices to imply all our main results in any dimension. In particular, I will explain why our Penrose-type inequality for the mass of an asymptotically Euclidean Kaehler manifold always still holds, given only this very weak metric fall-off hypothesis.
 

We find a new duality for form factors of lightlike Wilson loops in planar N=4 super-Yang-Mills theory. The duality maps a form factor involving an n-sided lightlike polygonal super-Wilson loop together with m external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analytic continuation from Minkowski to Euclidean space. We illustrate all of these subtleties explicitly in the simplest non-trivial NMHV-like case.

Quantum fields can sometimes have negative energy density.  In gravitational contexts, this threatens to permit both causality violations (such as traversable wormholes, warp drives, and time machines) and violations of the Second Law for black holes.  I will discuss the thermodynamic principles that rule out such pathological situations.  These principles have led us to an interesting lower bound on the energy flux, even for field theories in flat spacetime! This Quantum Null Energy Condition has now been proven for all relativistic field theories.  I will give an intuitive argument explaining why such ``quantum energy conditions'' ought to hold. 
 

  Our understanding of physical phenomena is intimately linked to the way we understand the relevant observables describing them. While a big deal of progress has been made for processes occurring in flat space-time, much less is known in cosmological settings. In this context, we have processes which happened in the past and which we can detect the remnants of at present time. Thus, the relevant observable is the late-time wavefunction of the universe. Questions such as "what properties they ought to satisfy in order to come from a consistent time evolution in cosmological space-times?", are still unanswered, and are compelling given that in these quantities time is effectively integrated out. In this talk I will report on some recent progress in this direction, aiming towards the idea of a formulation of cosmology "without time". Amazingly enough, a new mathematical structure, we called "cosmological polytope", which has its own first principle definition, encodes the singularity structure we ascribe to the perturbative wavefunction of the universe, and makes explicit its (surprising) relation to the flat-space S-matrix. I will stress how the cosmological polytopes allow us to: compute the wavefunction of the universe at arbitrary points and arbitrary loops (with novel representations for it); interpret the residues of its poles in terms of flat-space processes; provide a  general geometrical proof for the flat-space cutting rules; reconstruct the perturbative wavefunction from the knowledge of the flat-space S-matrix and a subset of symmetries enjoyed by the wavefunction.

The classical theory of integration concern integrals of differential forms over domains of integration. In geometric terms, this corresponds to a canonical pairing between de Rham cohomology and singular homology. For varieties defined over the reals, one can make use of complex conjugation to define a real-valued pairing between de Rham cohomology and its dual, de Rham homology. The corresponding theory of integration, that we call single-valued integration, pairs a differential form with a `dual differential form’. We will explain how single-valued periods are computed and give an application to superstring amplitudes in genus zero. This is joint work with Francis Brown.
 

Six-dimensional theories provide a unification of four-dimensional theories via dimensional reduction  together with access to some of the novel features arising from M-theory.  Ambitwistor strings directly generate S-matrices for massless theories in terms of formulae that localize on the solutions to the scattering equations; algebraic equations that determine n points on the Riemann sphere from n massless momenta.  These are sufficient to provide compact formulae for tree-level S-matrices for bosonic theories. This talk introduces their extension to the polarized scattering equations which arise from twistorial versions on ambitwistor-strings.  These lead to simple explicit formulae for superamplitudes in 6D for super Yang-Mills, supergravity, D5 and M5 branes and massive superamplitudes in 4D.  The framework extends also to 10 and 11 dimensions.  This is based on joint work with Yvonne Geyer, arxiv:1812.05548 and 1901.00134. 

Mysteries of isolated horizons: the Near Horizon Geometry equation, geometric characterizations of the non-extremal Kerr horizon, spacetimes foliated by non-expanding horizons.

3-dimensional null surfaces  that are  Killing horizons to the second order  are  considered. They are embedded in 4-dimensional spacetimes that satisfy the vacuum Einstein equations with arbitrary cosmological constant. Internal geometry of 2-dimensional cross sections of  the horizons  consists of induced metric tensor and a rotation 1-form potential. It is subject to the type D equation. The equation is interesting from the both, mathematical and physical points of view. Mathematically it  involves  geometry, holomorphic structures and algebraic topology.  Physically, the equation knows the secrete of black holes: the only  axisymmetric solutions on topological sphere  correspond  to the the Kerr / Kerr-de Sitter / Kerr-anti-de-Sitter non-extremal black holes or to the near horizon limit  of the extremal ones.  In the case of bifurcated  horizons the type D equation implies another spacial  symmetry. In this way the axial symmetry may be ensured without the rigidity theorem. The type D equation does not allow rotating horizons of topology different then that of the  sphere (or its quotient). That completes a new local non-her theorem. The type D equation is also  an integrability condition for the  Near Horizon Geometry equation and leads to new results on the solution existence issue.
 

I will talk about the implications of UV completion of quantum gravity on the low energy spectrums. I will introduce the constraints on low-energy effective theory due to unitarity and analyticity of scattering amplitudes, in particular an infinite set of new unitarity constraints on the forward-limit limit of four-point scattering amplitudes due to the work of Arkani-Hamed et al. In three dimensions, we find the constraints imply that light states with charge-to-mass ratio z greater than 1 can only be consistent if there exists other light states, preferably neutral. Applied to the 3D Standard Model like spectrum, where the low energy couplings are dominated by the electron with z \sim 10^22, this provides a novel understanding of the need for light neutrinos.

I will review the fishnet model, which is an integrable scalar QFT, obtained by an extreme gamma deformation of N=4 super Yang-Mills. The theory has a peculiar perturbative expansion in which many quantities at a fixed loop order are given by a single Feynman diagram. This feature allows the reinterpretation of Feynman loop integrals as integrable systems.

Massless Quantum Field Theories can be described perturbatively by chiral worldsheet models - the so-called Ambitwistor Strings. In contrast to conventional string theory, where loop amplitudes are calculated from higher genus Riemann surfaces, loop amplitudes in the ambitwistor string localise on the non-separating boundary of the moduli space. I will describe the resulting framework for QFT amplitudes from (nodal) Riemann spheres, building up from tree-level to two-loop amplitudes.
 

One of the main open problems in loop quantum gravity is to reconcile the fundamental quantum discreteness of space with general relativity in the continuum. In this talk, I present recent progress regarding this issue: I will explain, in particular, how the discrete spectra of geometric observables that we find in loop gravity can be understood from a conventional Fock quantisation of gravitational edge modes on a null surface boundary. On a technical level, these boundary modes are found by considering a quasi-local Hamiltonian analysis, where general relativity is treated as a Hamiltonian system in domains with inner null boundaries. The presence of such null boundaries requires then additional boundary terms in the action. Using Ashtekar’s original SL(2,C) self-dual variables, I will explain that the natural such boundary term is nothing but a kinetic term for a spinor (defining the null flag of the boundary) and a spinor-valued two-form, which are both intrinsic to the boundary. The simplest observable on the boundary phase space is the cross sectional area two-form, which generates dilatations of the boundary spinors. In quantum theory, the corresponding area operator turns into the difference of two number operators. The area spectrum is discrete without ever introducing spin networks or triangulations of space. I will also comment on a similar construction in three euclidean spacetime dimensions, where the discreteness of length follows from the quantisation of gravitational edge modes on a one-dimensional cross section of the boundary.
The talk is based on my recent papers: arXiv:1804.08643 and arXiv:1706.00479.
 

The study of isolated systems has been vastly successful in the context of vanishing cosmological constant, Λ=0. However, there is no physically useful notion of asymptotics for the universe we inhabit with Λ>0.  The full non-linear framework is still under development, but some interesting results at the linearized level have been obtained. I will focus on the conceptual subtleties that arise at the linearized level and discuss the quadrupole formula for gravitational radiation as well as some recent developments.  

Non-abelian gauge theories underly particle physics, including collision processes at particle accelerators. Recently, quantum scattering probabilities in gauge theories have been shown to be closely related to their counterparts in gravity theories, by the so-called double copy. This suggests a deep relationship between two very different areas of physics, and may lead to new insights into quantum gravity, as well as novel computational methods. This talk will review the double copy for amplitudes, before discussing how it may be extended to describe exact classical solutions such as black holes. Finally, I will discuss hints that the double copy may extend beyond perturbation theory. 

Over 50 years ago, Bondi, Sachs, Newman, Penrose and others laid down foundations for the theory of gravitational waves in full non-linear general relativity. In particular, numerical simulations of binary mergers used in the recent discovery of gravitational waves are based on this theory. However, over the last 2-3 decades, observations have also revealed that the universe is accelerating in a manner consistent with the presence of a positive cosmological constant $\Lambda$. Surprisingly, it turns out that even the basic notions of the prevailing theory of gravitational waves --the Bondi news, the radiation field, the Bondi-Sachs 4-momentum-- do not easily generalize to this context, {\it no matter how small $\Lambda$ is.} Even in the weak field limit, it took a hundred years to find an appropriate generalization of Einstein's celebrated quadrupole formula to accommodate a positive cosmological constant. I will summarize the main issues and then sketch the current state of the art.
 

In this talk, we will discuss some recent progress on the study of six-dimensional S-matrices as well as their applications. Six-dimensional theories we are interested include the world-volume theories of single probe M5-brane and D5-brane, as well as 6D super Yang-Mills and supergravity. We will present twistor-string-like formulas for all these theories, analogue to that of Witten’s twistor string formulation for 4D N=4 SYM. 
As the applications, from the 6D results we also deduce new formulas for scattering amplitudes of theories in lower dimensions, such as SYM and supergravity in five dimensions, and 4D N=4 SYM on the Columbo branch. 
 

I will present a procedure for perturbatively constructing the field content of gravitational theories from a convolutive product of two Yang-Mills theories. A dictionary "gravity=YM * YM" is developed, reproducing the symmetries and dynamics of the gravity theory from those of the YM theories. I will explain the unexpected, yet crucial role played by the BRST ghosts of the YM system in the construction of gravitational fields. The dictionary is expected to develop into a solution-generating technique for gravity.
 

There have been enormous advances in both our ability to represent scattering amplitudes at the integrand-level (for an increasingly wide variety of quantum field theories), and also in our integration technology (and our understanding of the functions that result). In this talk, I review both sides of these recent developments. At the integrand-level, I describe the "prescriptive" refinement of generalized unitarity, and show how closed, integrand-level formulae can be given for all leading-weight contributions to any amplitude in any quantum field theory. Regarding integration, I describe some new results that could be summarized as "dual-conformal sufficiency": that all planar, ultraviolet-finite integrands can be regulated and computed directly in terms of manifestly dual-conformal integrals. I illustrate the power of having such representations, and discuss the role played by a (conjectural) cluster-algebraic structure for kinematic dependence. 

I will explain a new proof of the non-linear stability of the Minkowski spacetime as a solution of the Einstein vacuum equation. The proof relies on an iteration scheme at each step of which one solves a linear wave-type equation globally. The analysis takes place on a suitable compactification of $\mathbb{R}^4$ to a manifold with corners whose boundary hypersurfaces correspond to spacelike, null, and timelike infinity; I will describe how the asymptotic behavior of the metric can be deduced from the structure of simple model operators at these boundaries. This talk is based on joint work with András Vasy.

I will describe how to recast perturbative quantum gravity using non-perturbative techniques from conformal field theory, focussing on the case of N=4 super Yang-Mills theory. By resolving the degeneracy among double trace operators at large N we are able to bootstrap one-loop supergravity corrections from the OPE of the CFT.
 

We study the winding mode sector of recently discovered string theories, which were, until now, believed to describe only conventional field theories in target space. We discover that upon compactification winding modes allows the string to acquire an oscillator spectrum giving rise to an infinite tower of massive higher-spin modes. We study the spectra, S-matrices, T-duality and high-energy behaviour of the bosonic and supersymmetric models. In the tensionless limit, we obtain formulae for amplitudes based on the scattering equations. The windings decouple from the scattering equations but remain in the integrands. The existence of this winding sector shows that these new theories do have stringy aspects and describe non-conventional field theories.  This talk is based on https://arxiv.org/abs/1710.01241.

Scattering amplitudes computed at a fixed loop order, along with any other object computed in perturbative QFT, can be expressed as a linear combination of a finite basis of loop integrals. To compute loop amplitudes in practise, such a basis of integrals must be determined. In this talk I introduce a new algorithm for finding bases of loop integrals and discuss its implementation in the publically available package Azurite.

I will discuss recent developments in the study of scattering amplitudes in Einstein-Yang-Mills theory. At tree level we find new structures at higher order collinear limits and novel connections with amplitudes in Yang-Mills theory using the CHY formalism. Finally I will comment on unitarity based observations regarding one-loop amplitudes in the theory. 

We consider two-dimensional chiral, first-order conformal field theories governing maps from the Riemann sphere to the projective light cone inside Minkowski space -- the natural setting for describing conformal field theories in two fewer dimensions. These theories have a SL(2) algebra of local bosonic constraints which can be supplemented by additional fermionic constraints depending on the matter content of the theory. By computing the BRST charge associated with gauge fixing these constraints, we find anomalies which vanish for specific target space dimensions. These critical dimensions coincide precisely with those for which (biadjoint) cubic scalar theory, gauge theory and gravity are classically conformally invariant. Furthermore, the BRST cohomology of each theory contains vertex operators for the full conformal multiplets of single field insertions in each of these space-time CFTs. We give a prescription for the computation of three-point functions, and compare our formalism with the scattering equations approach to on-shell amplitudes.

Superradiance in black hole spacetimes is a phenomenon by which a field of spin 0 or 1 can extract energy from the background. Typically, one can imagine sending a wave packet with a given energy towards a black hole and receiving in return a superposition of wave packets carrying a total amount of energy that is larger than the energy sent in. It can be caused by rotation or by interaction between the charges of the black hole and the field. In the first case, the region where superradiance takes place (the ergoregion) has a clear geometrical localization depending only on the physical parameters of the black hole. For charge induced superradiance, this is not the case and we have a generalized ergoregion depending also on the physical properties of the field (mass, charge, angular momentum). In the most severe cases, the generalized ergoregion may cover the whole exterior of the black hole. We focus on charge-induced superradiance for spin 0 fields in spherically symmetric situations. Alain Bachelot wrote a thorough theoretical study of this question in 2004, which, to my knowledge, is the only work of its kind. When I was in Bordeaux, he and I discussed the possibility of investigating superradiance numerically. Over the years it became an actual research project, involving Laurent Di Menza and more recently Mathieu Pellen, of which this talk is an account. The idea was to observe numerically some superradiant behaviours and gain a more precise understanding of the phenomenon. We shall show an exact analogue of the Penrose process with the superradiance of wave packets and a slightly different behaviour for fields "emerging" inside the ergoregion. We shall also explore the related question of black hole bombs and present some recent observations. 

Shortly after Mason & Skinner introduced the so-called ambitwistor strings, Berkovits came up with a pure-spinor analogue of the theory, which was later shown to provide the supersymmetric version of the Cachazo-He-Yuan amplitudes. In the heterotic version, however, both models give somewhat unsatisfactory descriptions of the supergravity sector.

In this talk, I will show how the original pure-spinor version of the heterotic ambitwistor string can be modified in a consistent manner that renders the supergravity sector treatable. In addition to the massless states, the spectrum of the new model --- which we call sectorized heterotic string --- contains a single massive level. In the limit in which a dimensionful parameter is taken to infinity, these massive states become the unexpected massless states (e.g. a 3-form potential) first encountered by Mason & Skinner."

  Any constant-scalar-curvature Kaehler (cscK) metric on a complex surface may be viewed as a solution of the Einstein-Maxwell equations, and this allows one to produce solutions of these equations on any 4-manifold that arises as a compact complex surface with even first Betti number. However, not all solutions of the Einstein-Maxwell equations on such manifolds arise in this way. In this lecture, I will describe a construction of new compact examples that are Hermitian, but not Kaehler.
 

Some recent applications of supertwistors to superparticle mechanics will be reviewed.
First: Supertwistors allow a simple quantization of the  N-extended 4D massless superparticle, and peculiarities of massless 4D supermultiplets can then be explained by considering the quantum fate of a classical ``worldline CPT'' symmetry. For N=1 there is a global CPT anomaly, which explains why there is no CPT self-conjugate supermultiplet. For N=2 there is no anomaly but a Kramers degeneracy explains the doubling of states in the CPT self-conjugate hypermultiplet.
Second: the bi-supertwistor formulation of the N-extended massive superparticle in 3D, 4D and 6D makes manifest a ``hidden’’ 2N-extended supersymmetry. It also has a simple expression in terms of hermitian 2x2 matrices over the associative division algebras R,C,H.
Third: omission of the mass-shell constraint in this 3D,4D,6D bi-supertwistor action yields, as suggested  by holography, the action for a supergraviton in 4D,5D,7D AdS. Application to the near horizon AdSxS geometries of the M2,D3 and M5 brane confirms that the graviton supermultiplet has 128+128 polarisation states. 

 Locality is not expected to be a fundamental aspect of a full theory of quantum gravity; it should be emergent in an appropriate semiclassical limit.  In the context of general holography, I'll define a new construct - the causal state - which provides a necessary and sufficient condition for a boundary state to have a holographic semiclassical dual causal geometry (and thus be "local").  This definition illuminates some general features of holographic quantum gravity: for instance, I'll show that the emergence of locality is "all or nothing" in the sense that it exhibits features of quantum error correction and quantum secret sharing.  In the special case of AdS/CFT, I'll also argue that the causal state is the natural boundary dual to the so-called causal wedge of a region. 

This talk is about a 4d "(ambi-)twistor string" formula for sEYM tree-level scattering amplitudes and is work in progress. The formula sheds some new light on the translation between CHY formulae and (ambi-)twistor formulae in general, potentially even at loop level.

In this talk, I discuss the positive geometry of the Wilson Loop Diagrams appearing in SYM N-4 theory. In particular, I define an algorithm for associating Wilson Loop diagrams to convex cells of the positive Grassmannians. Using combinatorics of these cells, I then consider the geometry of N^2MHV diagrams on 6 points.