​​Conformal blocks are the building blocks of conformal field theories, the key ingredients of correlation functions and knowledge of these blocks is central to the conformal bootstrap. This lecture covers some general results before quickly specialising to two-dimensions. It discusses the implications of global conformal invariance and then the larger and more constraining Virasoro algebra symmetry. It introduces various methods of calculation including brute force, differential equations, recursion relations and closed formulae - and some aspects of bootstrap techniques.

We briefly overview how historically string theory led theoretical physics first to algebraic/differential geometry, and then to computational geometry, and now to data science. Using the Calabi-Yau landscape - accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades - as a starting-point and concrete playground, we then launch to review our recent programme in machine-learning mathematical structures and address the tantalizing question of how AI helps doing mathematics, ranging from geometry, to representation theory, to combinatorics, to number theory. Zoom Link: https://us02web.zoom.us/j/83496714171?pwd=bld3QmQ2c21laWxEWTd6ejVQbjZ5dz09 (contact dionysios.anninos@kcl.ac.uk for password)

In has become clear in recent years that working in sectors of large global charge of strongly coupled and otherwise inaccessible CFTs leads to important simplifications. It is indeed possible to formulate an effective action in which the large charge appears as a control parameter. In this talk, I will explain the basic notions of the large-charge expansion using the simple example of the O(2) model and then generalize to models with a richer structure which showcase other effects. [For the zoom link please email alejandro.cabo_bizet@kcl.ac.uk]

In this talk we will study type-B conformal anomalies associated with 1/2-BPS Coulomb-branch operators in 4D N=2 SCFTs. We will derive the conditions under which these anomalies can match across the conformal phase and the Higgs phase, and explicitly see them at work in concrete examples of both matching and non-matching. On the one hand matching leads to a new class of data on the Higgs branch of 4D N=2 SCFTs that are exactly computable. On the other, non-matching imposes novel restrictions on the holonomy of the conformal manifold. [For the Zoom link, please email to: alejandro.cabo_bizet@kcl.ac.uk ]

In this talk I will present the use of resurgence techniques in identifying non-perturbation physics and its relation to renormalons, in light of recent work of Marcos Mariño and me. This exploration has touched 1+1 QFTs and condensed matter systems, revealing that the presence of renormalons is more widespread than expected. After introducing both ideas in the title, I will specialise in the case of the 1D fermion gas with dirac-delta attractive potential. This case is a clean example of our approach and unveils a curious interplay between resurgence, renormalons, and superconductivity. [Please email damian.galante@klc.ac.uk for the link]

In this talk, we will discuss recent progress in understanding quantum gravity amplitudes (partition function and boundary correlation functions) in Liouville gravity, and how they limit to Jackiw-Teitelboim (JT) correlators. We also discuss multiboundary and higher genus amplitudes. We focus on two main results: the Liouville gravity answers look like q-deformations of the JT answers, and Liouville gravity can be related to a 2d dilaton gravity with a sinh dilaton potential. We end with discussions on supersymmetric extensions and work in progress. Based largely on arXiv:2006.07072 and 2007.00998​. [For the Zoom link, please email to: alejandro.cabo_bizet@kcl.ac.uk ]

A simple probe of chaos and operator growth in many-body quantum systems is the thermal out of time ordered (OTO) four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside a so called butterfly cone. I will discuss universal features of the spatiotemporal structure of this exponential growth in large N systems. In particular I will argue that there can be a smaller, “scramblon” cone inside the butterfly cone. Outside the scramblon cone, the growth of the OTO four point function is completely universal and saturates a chaos bound. I will explain the connection to conformal Regge theory, where crossing the scramblon cone is related to an exchange of dominance between the pomeron and the stress tensor. Finally, I will discuss a connection between chaos and energy transport, called the pole skipping phenomenon, which is a subtle effect in the thermal energy density retarded two point function at a special point in the complex frequency and momentum planes. I will present an improved understanding of this connection and test it in the large q limit of an SYK chain, where I determine both the Lyapunov growth of the OTO correlator and the energy density two point function exactly as a function of the coupling, interpolating between weekly coupled and maximally chaotic behaviour. [For the Zoom link, please email to: alejandro.cabo_bizet@kcl.ac.uk ]

In CFT, the expressions for Euclidean 3-point functions in momentum space were fully obtained in recent years, but their Lorentzian counterparts have remained quite unknown. In this talk I will present the expression for the Lorentzian 3-point function of scalars, and further show a way to obtain tensorial ones. As I will argue, such momentum-space expressions simplify considerably the computation of the expectation values of the ANEC (Average Null Energy Condition) operator on the states used in the conformal colliders setting, whose positivity has been used to put interesting bounds on conformal anomalies. With the motivation of generalising these bounds and studying the implications of the ANEC for QFT, I will discuss perturbative corrections to the simplest ANEC expectation values in lambda-phi4 theory. [For the Zoom link, please email to: alejandro.cabo_bizet@kcl.ac.uk ]

In this talk I discuss some work in progress concerning higher-derivative (HD) terms in 4d supergravity. In particular we'll focus on the simplest case of 4-derivative terms appearing in minimal gauged supergravity. This choice minimizes the freedom in the HD terms to two arbitrary constants, which can be determined by a holographic match. This gives a prediction about the reduction of 11d HD terms on S^7. We then derive holographic predictions for the first subleading terms of various supersymmetric partition functions in their expansion of the gauge group rank, N. Additionally we are able to evaluate the on-shell action for non-BPS solutions in supergravity, allowing us to discuss black hole thermodynamics in the presence of HD terms. (To request the Zoom link send email with empty text and subject "talk" to alejandro.cabo_bizet@kcl.ac.uk)

I will try to provide an overview of the papers 1605.01070, 1612.00391 and most recently 2003.08409, where progress is made in determining how the bulk metric of a holographic spacetime can be reconstructed purely from boundary data. My focus will be in the results of the first reference 1605.01070, which provides the framework for the other works. Link to meeting: here

I will discuss the recent paper 2003.02770 with the title above (by J. Nian and L. Pando Zayas). Link to meeting: here

TBA

Join here (you need Microsoft Teams). Typical systems of many particles in strong interaction have extremely complex behaviours which are hard to study in detail. But when the system is very large, simplicity resurfaces: typically just a few degrees of freedom are relevant, which follow new, simple laws. Understanding what the emergent behaviours are from the underlying microscopic interactions is one of the foremost problems in modern science. A very powerful set of ideas and tools at our disposal is hydrodynamics. Although the Navier-Stokes and related equations have been studied for a very long time, we are now starting to uncover the full potential of the fundamental principles of hydrodynamics. In particular, in a recent breakthrough it was understood how to apply these principles to quantum and classical integrable models, where infinitely many conserved currents exist, giving ``generalised hydrodynamics”. I will overview the fundamental principles of hydrodynamics and their adaptation to integrable systems, with simple examples such as the quantum Lieb-Liniger model, the classical Toda model, and the soliton gases. I will discuss a recent cold-atom experiment that confirmed generalised hydrodynamics, and, if time permits, show some of the exact results that can be obtained with this formalism, such as exact nonequilibrium steady states and exact asymptotic of correlation functions at large space-time separations.

We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). The key lies in relating standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutations in the system of identical bosons --- is crucial in either case. This viewpoint may have implications for confinement at finite N, and for quantum gravity via gauge/gravity duality. As a byproduct, we obtain a characterization of the partially-confined/partially-deconfined phase at finite coupling: the constant offset of the distribution of the phases of the Polyakov loop is the order parameter.

I will review the relation between symmetries and charges and explain how this works in the context of gravity. I will then explain how dual charges can be derived from a similar procedure.

The principles of Lorentz invariance, locality and unitarity highly constrain the physics at accessible high energy: the type of interactions allowed as well as most of the theorems known in particle physics are instances of these principles. This is neatly seen in the structure of scattering amplitudes in asymptotically flat space-times. However, cosmology suggests that such principles may be just approximate: Lorentz invariance is broken at cosmological scales and the accelerated expansion of the universe seems to prevent a full-fledge definition of quantum mechanical observables. If our fundamental ideas in particle physics become somehow approximate in cosmology, what are the fundamental rules governing cosmological processes? In this talk I will report on a recent program which aims to address this question, by bringing both philosophy and methods which have been successful for scattering amplitudes to the analysis of cosmological observables. In particular we investigate the analytic properties of the perturbative wavefunction of the universe, how fundamental physics is encoded into it, how the flat-space physics reflects into it, and how all these features are encoded into new mathematical structures, which can be used as a novel first principle definition of the perturbative wavefunction.

In this talk I will explore the space of two-to-two S-matrices in two-dimensional theories with a global O(N) symmetry, as restricted by the general principles of unitarity, crossing and analyticity. I will describe various features of the allowed space and identify some special points on its boundary with known integrable theories. Finally, I will present a useful dual formulation of the S-matrix bootstrap problem. Based on arXiv:1909.06495.

The correlation functions (three and higher point) in N=4 SYM can be computed using integrability techniques. One formalism is called hexagonalization and its main object is an integrable form-factor with hexagonal shape. It was successfully used to compute a specific all loop four-point function for the first time. However, it seems that new developments are needed to understand the five-point function and other kinds of finite size corrections. In this talk, after a long review of the hexagonalization procedure, I will explain the five-point calculation at weak coupling and its difficulties.

Finding a theoretical framework to explain how phenomenological transport laws on macroscopic scales emerge from microscopic deterministic dynamics poses one of the most significant challenges of condensed matter physics. In recent years, the advent of the generalized hydrodynamics in integrable quantum systems and more recent studies of quantum chaos and its relation to transport, reinvigorated the field of nonequilibrium physics in spin chains. Numerous results were found: lower bounds to diffusion constants, exact expressions for diffusion coefficients and remarkable anomalous features of transport in quantum and classical chains, deeply related to the Kardar-Parisi-Zhang dynamical universality class. I will present an overview of such results with a particular focus on anomalous transport and its relation to non-linear hydrodynamics.

TBA