Abstract: In this talk I will review some recent developments in computing holographic correlators at large N. I will focus on the four-point function of half-BPS operators in two SCFTs, namely N=4 SYM in 4d and N=2 SYM in 4d with flavour group G_F. Via AdS/CFT, these are dual to graviton scattering in AdS_5\times S^5 and gluon scattering in AdS_5\times S^3 background, respectively. Despite the apparent complexity, the tree-level dynamics of both theories is actually extremely simple, due to the existence of a hidden conformal symmetry. The results are better cast in terms of a generalised Mellin transform which makes manifest many properties of the associated AdS amplitudes, such as large p limit, double-copy, colour-kinematic and BCJ relations.

Abstract: In this talk I will suggest a new approach to scattering theory in flat space. The basic observation is that the Poincaré group is realised both as isometries of Minkowski space but also as a group of conformal isometries of null infinity. Our experience with AdS/CFT has therefore prompted the hope that some QFTs in Minkowski spacetime may be dual to some exotic CFTs at null infinity, a topic referred to Celestial/Carrollian holography. I will advocate for the “Carrollian conformal bootstrap” as a new framework to make these ideas very concrete and calculable, and which should broadly apply to any theory of massless particles. As a first step I will explain how Carrollian conformal fields most naturally encode the unitary irreducible representations of the Poincaré group (aka Wigner’s particles). Then I will turn to the classification of two- and three-point correlations functions of such Carrollian fields and relate them to bulk observables. I will finally mention the next steps towards the Carrollian conformal bootstrap: OPE expansion, conformal block decomposition, crossing equations, etc.

Abstract: In a series of recent works it has become clear that quantum scattering amplitudes can be used to gain surprisingly useful insights to the dynamics of Kerr black holes. A simple infinite family of three-point amplitudes have been found, which describes the primary gravitational interaction of a black hole with quantum spin s. However, the corresponding Compton four-point amplitudes are not known except for a few low-spin examples. These amplitudes are needed for post-Newtonian and post-Minkowskian calculations of inspiraling binary black-hole systems. In this talk, I will show that the Kerr three-point amplitudes can be uniquely predicted from the principle of gauge symmetry. In particular, I will discuss the construction of a family of EFTs with Stuckelberg higher-spin fields that describe the expected dynamics of Kerr black holes. The EFTs enjoys massive higher-spin gauge symmetry, which is used as a selection principle for the non-minimal interactions. I will also show upcoming results for the Compton amplitude to all orders in spin, and discuss the matching to explicit GR calculations.

Abstract: Inflation is the leading paradigm for explaining the origin of primordial fluctuations which seeds the creation of galaxies. These primordial fluctuations are encoded in a cosmological wavefunction. In this talk I will discuss how to compute the wavefunction using the cosmological bootstrap, which is a series of constraints from fundamental physical principles. These include unitarity, which results in the cosmological optical theorem, as well as locality, which results in the manifest locality test. I will then show how these principles can be used to establish no go theorems for parity odd interactions. In the end I will talk about the analytic wavefunction, where we attempt to follow in the S-matrix program and write down dispersion relations for the wavefunction. This paves the way to establishing positivity bounds for cosmology and linking observables in cosmology to fundamental principles.

Abstract: We shall consider a crossing equation of the Euclidean conformal group in terms of conformal partial waves and in particular, a position independent representation of this equation. We shall briefly discuss the relevance of this equation to the problem of cosmological bootstrap. Thereafter, we shall sketch the derivation of the Biedenharn-Eliiot identity (a pentagon identity) for the 6j symbols of the conformal group and show how this provides us with an exact solution to said crossing equation. For the conformal group (which is non-compact), this involves some careful bookkeeping of the spinning representations. Finally, we shall discuss some consistency checks on the result obtained, and some open questions.

Abstract: The double copy programme aims to construct gravitational quantities from suitably defined “products” of analogous quantities in gauge theory. It was initially developed in the context of scattering amplitudes and hence appears biased towards perturbation theory in flat backgrounds. I will give an overview of recent efforts to extend the double copy beyond flat spacetimes, and beyond scattering amplitudes, and comment on possible connections to cosmology and holography.

Abstract: Superrotations of four-dimensional asymptotically flat spacetimes extend the standard BMS group and are pivotal in the realization of the so-called Celestial CFT (CCFT), exotic two-dimensional CFT putatively dual to 4D AF gravity. In the first tale, based on work soon to appear, I propose that superrotations can be used to holographically compute CCFT twist field correlators and Entanglement (pseudo-)Entropy. In the second tale, I abandon holography and move to higher dimensions. I discuss the most general asymptotic solution of Ricci flat gravity with null boundary in any dimension and the work, recently appeared, on its reduction – in even dimensions – to a phase space with renormalized supertranslation and superrotation charges.

Abstract: Locality is a powerful property of quantum field theory and implies that information can be strictly localized in regions of space, and is completely inaccessible from far away. On the other hand, the holographic nature of quantum gravity suggests that the theory is ultimately non-local and that information can never be localized deep inside some spacetime region, but rather is always accessible from the boundary. This is meant to hold as a fully non-perturbative statement, but the fate of locality in G_N perturbation theory is unclear. To investigate locality in quantum gravity, an important first step is to define candidate local operators. The challenge is that to be diffeomorphism-invariant, i.e. to respect the gravitational Gauss law, such operators must be gravitationally dressed which usually makes them non-local. In this talk, I will discuss the incarnation of this problem in the context of AdS/CFT and propose a set of operators which appear to be local to all orders in G_N perturbation theory. Such operators can only be defined around sufficiently complicated CFT states, for reasons that I will explain. I will also comment on the connection of this framework to the introduction of an observer in de Sitter space.

Abstract: I will review our current understanding of the initial conditions of the universe, and describe what information is available from current and future measurements of cosmological correlation functions. Then I will describe a new set of techniques developed to compute and constrain the possible shapes of those correlation functions. Finally, I will describe a toy example of emergent time in cosmological correlations. 

Abstract: Symmetries are one of the major tools to understand the structure of physical theories. But even the most powerful symmetry is useless if it is hidden and therefore not accessible in calculations. Prominent examples are S-, T- and U-dualities of superstrings and branes. We know that they unify the five perturbative superstring theories and M-theory into a single framework, but their imprints on the low-energy effective supergravity theories are subtle and easy to miss. A framework which addresses this issue is (exceptional) generalized geometry. Although thought as a natural extension of geometry to an extended tangent bundle, it still lacks fundamental objects of differential geometry like a Riemann tensor. After a short review of the most important differences between generalized and standard differential geometry, I will present the underlying cause for this trouble and present a proposal for a solution which gives a new, geometric perspective on duality symmetries in supergravity. This approach will not just resolve some old puzzles but it also has direct applications, leading to a much broader notion of dualities in supergravity that can be used to generate new solutions using a tool known as consistent truncations.

Abstract: Many recent successes in holography, including microstate counting for Anti-de-sitter black holes or the determination of partition functions of the dual conformal field theory, involve extremization problems. The quantities to extremize are anomalies and supersymmetric indices, which are renormalisation group invariants and are independent of small deformations of the theory. It is natural to ask what is the gravitational dual of such quantities. In this talk, we provide a general proposal based on geometry and show that  the so-called equivariant volume of the internal manifold can be used to characterize universally the geometry of a large class of supersymmetric solutions in holography.