Academic Year 2021/2022

In this talk, I will present exact expressions for integrated correlators of four BPS operators in N=4 supersymmetric Yang-Mills (SYM) for classical gauge groups, G_N. I will show that they can be expressed as a simple two-dimensional lattice sum, which is a function of N and of the complex Yang-Mills coupling \tau=\theta/2\pi + i 4\pi/g^2_{YM}. This expression contains infinite orders of perturbative and non-perturbative instanton terms, and manifests the Goddard-Nuyts-Olive duality of N=4 SYM. Furthermore, the integrated correlators satisfies striking 'Laplace difference' equations, which determines the integrated correlators for all classical gauge groups in terms of the SU(2) correlator. I will also comment on matching our results with the standard Feynman diagram computation, and the relation to four-graviton amplitude in type IIB superstring in AdS space.

Studies of gravitational waves have been devoted mostly to sources such as binary black hole mergers or neutron star mergers, or generally sources that are stationary outside of a compact set. These systems are described by asymptotically-flat manifolds solving the Einstein equations with sufficiently fast decay of the gravitational field towards Minkowski spacetime far away from the source. Waves from such sources have been recorded by the LIGO/VIRGO collaboration since 2015. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields decay more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations both in the Einstein vacuum case and for neutrino radiation. The latter results are important for sources with extended neutrino halos.

The bootstrap approach to cosmological correlators relies on the existence of differential equations in terms of boundary momenta. I will describe a new method to efficiently characterize and (in some sense) explain the existence of these differential equations. The method is general, but I will focus on cosmological correlation functions of a light scalar in power law FLRW cosmologies. It recasts the differential equation in terms of a new (somewhat magical) object, a flat connection in the boundary kinematic space. The mathematical theory of this flat connection is beautiful on its own right, and not fully developed yet. The physical information it carries - in particular, locality of the correlator - is encoded in its structure in a way that I don’t understand.

Time-dependent orbifolds generated from Minkowski spacetime are very useful toy models to address the study of Big-Bang type singularities. After introducing their geometry, I will review some of the results presented in the literature when they have been considered as cosmological backgrounds of string theory. I will in particular discuss the most serious issue that has been encountered: the unusual divergences found in the computation of some tree-level string scattering amplitudes. I will then move to the study of an effective quantum field theory on these models, which shows where the real nature of their pathological behavior lies. Finally, in order to cure the divergences, I will introduce a noncommutative framework which seems promising both from the QFT and the string theory point of view.

Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general heuristic arguments) universally for all theories. Few are exact and inviolable. In this talk, I will present new methods for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. Concrete examples will include bounds that relate transport to quantum chaos through 'pole-skipping' as well as bounds without relation to chaos, such as the conformal bound on the speed of sound. I will also outline a set of general observations regarding the univalence properties of diffusion and sound in holographic models. Finally, I will discuss how these ideas could be generally applicable to constraining any effective field theory, not only hydrodynamics.

The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral boson and a chiral Majorana mode on the boundary. It has been recently conjectured that these two boundary modes are superpartners of each other and described by a supersymmetric conformal field theory. In this talk, I present a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective gravitino in the bulk. After breaking supersymmetry through a goldstino (i.e. a Nambu-Goldstone fermion), the gravitino becomes massive and can be seen as the neutral spin-3/2 collective mode that characterises the Moore-Read state in the bulk. After integrating out this massive fermion field, I obtain a purely bosonic topological action that properly encodes the Hall conductivity, Hall viscosity and gravitational anomaly, which represent the physical observables of the fractional quantum Hall effect.

Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension N. In this talk I will review the HT techniques and emphasise few key open problems. I will also discuss the recent efforts to extend these ideas to higher dimensions and for UV divergent relevant operators.

A feature of General Relativity is the interplay between physics and geometry. An beautiful instance of this fact is realised at null infinity where asymptotic gravitational data are realised geometrically as a boundary "conformal Carrollian geometry", with the BMS group acting as a group of symmetry. The invariant meaning (and geometrical elegance) lying behind these however only fully appear in the language of Cartan geometry. I will explain this as well as relationship to other related construction such as local twistors.

Since in gravity theories the massless particle with the highest spin is the graviton, we expect that all observables have a universal behaviour at high energy. In this talk I will first consider the deflection angle in the elastic scattering and how that, in this case, universality is obtained by adding the radiation reaction contribution to the part obtained from the potential region. Then I will consider the inelastic processes in which gravitons are emitted and, following the method of Bloch-Nordsieck, I will construct the eikonal operator for the emission of soft gravitons and I will use it to compute the soft waveforms and the zero-frequency limit (ZFL) of the spectrum of emitted gravitons. I will show that the previous observables are also universal but, in these inelastic cases, universality is reached in a more non-trivial way.

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 space-times near space-like infinity.

We establish a framework for computing graviton scattering amplitudes on curved self-dual radiative space-times; these are chiral, source-free, and asymptotically flat spaces, determined by free characteristic data at null infinity. Such space-times admit an elegant twistor description via Penrose's non-linear graviton, which manifests their underlying integrability. The tree-level S-matrix is written in terms of an integral over the moduli space of holomorphic maps from the Riemann sphere to twistor space, with the degree of the map corresponding to the helicity configuration of the external gravitons. For the MHV sector, we derive the amplitudes directly from general relativity, while other helicity configurations arise from a natural family of generating functionals and pass several consistency checks. The amplitudes exhibit many novel features which are absent in Minkowski space, including tail effects. Although there are residual integrals due to the functional degrees of freedom in the background space-time, our formulae have fewer such integrals than expected from space-time perturbation theory. In highly symmetric special cases, such as self-dual plane waves, the number of residual integrals can be further reduced, resulting in even simpler expressions for the scattering amplitudes. If there is time I will discuss connections with celestial holography. This is joint work with Tim Adamo and Atul Sharma based on 2203.02238, 2110.06066, 2103.16984, 2010.14996.

TBA

Feynman’s path integral is the most elegant known formulation of the quantum physics of continuous systems. It is particularly suited to relativistic theories, including gauge theories and gravity. However, it is an enduring embarrassment that path integrals have never been rigorously formulated except by ``Wick rotating'' to imaginary (``Euclidean'') time. Unfortunately, continuing back to real (Lorentzian) time, where observations are made, is usually impossible outside of perturbation theory. Moreover, the Euclidean path integral fails badly for gravity and therefore for cosmology. I will describe recent work with J. Feldbrugge aimed at defining and evaluating Lorentzian (i.e., real-time) path integrals, using new physical insights and an extension of Picard-Lefschetz (steepest descent) methods for finite-dimensional oscillatory integrals. Finally, I will summarise some exciting new work with L. Boyle using the path integral for cosmology to calculate the gravitational entropy of a semi-realistic universe. This calculation suggests a new, simpler explanation for the large scale geometry of space time.

I will discuss how fracton physics can be studied systematically within the geometric framework of Double Field Theory (DFT). Following an introductory review of fractons, I will argue that their restricted mobility and large degeneracy of quantum states can be attributed to the generalized geodesics and infinite-dimensional isometries present in non-Riemannian backgrounds of DFT. Furthermore, we find that a doubled pure Yang-Mills or Maxwell theory reduces to an ordinary one interacting with a strain tensor theory, giving a unifying description of photons and phonons. I will show how this photon-phonon theory, when minimally coupled to a charged particle in a non-Riemannian background, lifts the particle immobility to a saturation velocity and gives a modified dispersion relation.

I discuss the results from a series of papers on performing certain null reductions on coincident M5 branes. Starting with the most general result on curved backgrounds, before focusing on an interesting Omega-deformed spacetime. The latter is central to a construction that rebuilds the full 6d theory using instantons, I discuss this mechanism as well as the interesting symmetry groups at play.

In this talk I will review recent work on `decomposition,' a property of 2d theories with 1-form symmetries and, more generally, d-dim'l theories with (d-1)-form symmetries. Decomposition is the observation that such quantum field theories are equivalent to ('decompose into’) disjoint unions of other QFTs, known in this context as "universes.” Examples include two-dimensional gauge theories and orbifolds with matter invariant under a subgroup of the gauge group. Decomposition explains and relates several physical properties of these theories -- for example, restrictions on allowed instantons arise as a "multiverse interference effect" between contributions from constituent universes. First worked out in 2006 as part of efforts to understand string propagation on stacks, decomposition has been the driver of a number of developments since. In the first half of this talk, I will review decomposition; in the second half, I will focus on the recent application to anomaly resolution of Wang-Wen-Witten in two-dimensional orbifolds.

In the last few years, there has been enormous progress on the statistical description of the entropy of BPS black holes in AdS_D for 𝐷>3 in terms of states in the dual field theory. The success of such developments relies on the existence of an extremisation principle in the bulk which maps to the evaluation of the partition function in the field theory in the large charge limit. In this talk, I will describe an ''off-shell'' approach to the study of black hole thermodynamics in AdS_5 based on an effective superpotential. This approach offers a powerful tool to analyse the thermodynamics without resorting to explicit solutions and can be in principle implemented even to non-supersymmetric configurations. For BPS black holes, it provides the framework where the aforementioned (Hosseini-Hristov-Zaffaroni) extremisation principle emerges naturally in the bulk while it is also directly related to Sen’s entropy function for extremal black holes.

This will be a mostly expository talk to introduce mathematical physicists to some difficult problems of arithmetic geometry involving infinities that are conjectured to be 'regularizable.' The overall hope is that the maths/physics expertise can be of help in making progress on them.

Recently Leutheusser and Liu identified an emergent algebra of Type III1 in the operator algebra of N=4 super Yang-Mills theory for large N. Here we describe some 1/N corrections to this picture and show that the emergent Type III1 algebra becomes an algebra of Type II∞. The Type II∞ algebra is the crossed product of the Type III1 algebra by its modular automorphism group. In the context of the emergent Type II∞ algebra, the entropy of a black hole state is well-defined up to an additive constant, independent of the state. This is somewhat analogous to entropy in classical physics.

One can paraphrase Penrose’s strong cosmic censorship conjecture as stating that general relativity is generically a deterministic theory. While the full conjecture remains wide open there has long been evidence pointing towards its validity at least for small perturbations of exact rotating Kerr black holes. In this talk I will give a brief historical account of this evidence, discuss the analytic as well as the geometric aspects of this conjecture, and conclude by presenting forthcoming work on the linear instability of the Kerr Cauchy horizon.

Scattering amplitudes are very natural in (2,2) signature, where the on-shell three-point functions do not vanish. Motivated by recent progress in celestial holography, we link (2,2) scattering amplitudes to Black Holes in (2,2) Klein space, and study their global structure. The link is very natural from the perspective of twistor theory. These black holes are a simple analytic continuation away from (1,3) solutions, but their (2,2) signature unveils new properties such as a direct diffeomorphism between Kerr Taub-NUT and Taub-NUT spacetimes.

In this talk I will explain, in the example of Rozansky-Witten models with affine target spaces, how to reconstruct an (extended) TQFT from its identity defect. For illustration I will shoot a sparrow with a cannon and use defects to rederive the state spaces of affine RW models for arbitrary surfaces.

In this talk I will re-express the Nekrasov-Shatashvili free energy for a four-dimensional N=2 gauge theory as an integral of a ratio of Wronskians of solutions to the relevant oper equation, with the AD2 theory and the pure SU(2) theory as two main examples. This motivates the definition of a generalized Nekrasov-Shatashvili free energy for any four-dimensional N=2 theory of class S, and makes a connection with abelianization and exact WKB analysis. We will end with some remarks regarding the five-dimensional generalization and the relation to similar mathematical structures underlying the topological string partition function. This talk is based on 2109.14699 and work in progress.

Wilson lines are a prototypical example of defect in QFT. I will consider the defect CFT_1 defined by correlators of operator insertions on a supersymmetric Wilson line in the d=3 superconformal ABJM model, illustrating how superspace techniques, analytic bootstrap and direct Witten diagrammatics can be used, combined with holography, to find its CFT data. I will then present a nonperturbative definition of Mellin amplitude for more general CFT_1 four-point correlators, and describe the use of this formalism to derive new results.

Calabi-Yau metrics and hermitian Yang-Mills connections have played a key role in both mathematics and physics in recent decades, and are particularly important for deriving semi-realistic models of particle physics from string theory. Unfortunately, explicit expressions for these objects are few and far between, leaving us unable, for example, to compute particle masses or couplings in string models. I will review recent progress on using machine learning techniques to compute these quantities numerically, with a particular focus on the example of computing gauge connections on line bundles.

We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure such as probabilities, convexity, complex numbers, continuity, or dimension. We'll discuss the axioms, sketch the proof of the theorem, and survey open questions, further directions, and context. (Based on joint work with Andre Kornell arxiv:2109.07418.)

For quantum fields in curved spacetimes there isn't a unique notion of vacuum state and the in and out vacua might be different, therefore, to perform calculations with interacting theories we require the use of the Schwinger-Keldysh formulation, very similar to undergraduate quantum mechanics. However, the usual assumption that the theory is free at past infinity isn't necessarily true and there is a need to modify the usual formalism to take this into account, resulting in a 3x3 matrix of propagators instead of the more familiar 2x2. In my talk I will describe this new formalism and test it in flat spacetime with the surprising conclusion that even in Minkowski spacetime it seems like the theory isn't free at past infinity at finite temperature as is commonly assumed.

TBA

Classical gravitational interactions of spinning black holes (BHs) can be usefully described by certain limits of certain quantum scattering amplitudes, for massive higher-spin fields "minimally coupled" to gravity. Tree-level interactions between two BHs are determined by 3-point amplitudes (BH in, BH out, meeting one graviton) which are arguably well understood -- on the quantum side, for arbitrary-spin massive particles; classically, to all orders in the BH spin. Two-BH (conservative) interactions at the classical 1-loop level (and other processes) are argued to be determined by the additional 4-point "Compton" amplitude (BH in, BH out, meeting two gravitons), which is more poorly understood -- on the quantum side, up to spin-2 (or 5/2?); classically, up to 4th (or 5th?) order in the BH spin. In this talk, we'll discuss efforts to better understand the BH-graviton Compton amplitude for higher spins, and its applications, including directly interpreting its classical limit as the o utgoing amplitude for an incoming gravitational plane wave scattering off a Kerr BH.

A particle physics approach to describing black hole interactions is opening new avenues for understanding gravitational-wave observations. In this talk, we will review this paradigm change showing how general relativity naturally emerges from scattering amplitudes. Applications for deriving solutions to Einstein field equations, the bending of light and waveforms - directly from quantum field theory - are explained.

While multicenter black holes in asymptotically flat space have long been object of study, the construction of multi black holes geometries in Anti-de Sitter spacetimes remains so far elusive. In this talk I will discuss recent progress on the search for these solutions. Working in the probe approximation, I will show that there exist stable ad metastable black hole bound states in compactifications of M-theory on 7-dimensional Sasaki-Einstein manifolds with Betti multiplets and AdS4 vacua. I will map out their thermodynamic landscape and discuss the relevance of these setups for describing glassy systems via holography. I will finally discuss their supersymmetric limits, in light of recent developments regarding the entropy matching for stationary AdS4 black holes via localization in the dual 3d CFT.

Infinite towers of massive modes arise for every compactification of higher dimensional theories. Understanding the properties of these Kaluza-Klein towers on non-trivial solutions with an AdS factor has been a longstanding issue with clear holographic interest, as they describe the spectrum of single-trace operators of the dual CFTs at strong coupling and large N. In this talk, I will focus on two classes of solutions of such kind. The first class consists of AdS4 solutions of D=11 and Type II supergravity that can be obtained from maximal gauged supergravities in D=4. For the later part, I will describe new families of solutions in N=(1,1) supergravity in D=6 which uplift from half-maximal supergravity in D=3. In both cases, the spectra can be computed using recent techniques from Exceptional Field Theory, and the information thus obtained leads to several unexpected conclusions.