The S-matrix bootstrap can be used to carve out the space of physical theories. What can we say about the space of theories of quantum gravity based on this approach? Based on work with Andrea Guerrieri and Joao Penedones. Zoom link: https://zoom.us/j/94504664165?pwd=c3VmMDNsbkRwWWdoUUxIRDhUcjB4dz09 (for password email dionysios.anninos@kcl.ac.uk)

In this talk we will present a mechanism for accelerated expansion of the universe in the generic case of negative-curvature compactifications of M-theory, with minimal ingredients. M-theory on a hyperbolic manifold with small closed geodesics supporting Casimir energy, along with a single classical source (7-form flux), contains a 3-term structure for volume stabilization at positive potential energy. We find that a combination of warping and hyperbolic rigidity effects can stabilize the metric and form field. A simple generalization incorporating 4-form flux produces axion monodromy inflation, along with other forms of accelerated expansion. Our approach provides a simple uplift of the large-N M2-brane theory to de Sitter, and introduces new connections between mathematics and the physics of string/M theory compactifications. Zoom link: https://zoom.us/j/94504664165?pwd=c3VmMDNsbkRwWWdoUUxIRDhUcjB4dz09 (for password email dionysios.anninos@kcl.ac.uk)

Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this talk I will explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This approach gives a natural way to identify wormhole-like correlations, even for individual theories, in particular in theories with gravity duals. I will also discuss how to extend the Goldstone effective-field-theory approach to study operator correlation functions, and explain the relation of the EFT of quantum chaos to the bulk physics of wormhole-like geometries. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

I will explain a method of constructing BPS algebras for string theory on generic toric Calabi-Yau threefolds. The approach is a ``bootstrap” method based on the 3D colored crystals that describe BPS states of the system. The resulting algebras are quiver Yangians Y(Q,W) that are associated with the quiver and the superpotential of the theory. [Please email alejandro.cabo_bizet@kcl.ac.uk for zoom link]

Machine Learning has opened many new doors in science across multiple disciplines. Starting from recent work by the speaker and collaborators on in-depth explorations into the vacuum structure of gauged maximal supergravities using Machine Learning Technology, notably Google's TensorFlow library, we subsequently take a broader perspective on what happens when Machine Learning meets Physics. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

We derive an explicit map between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two and to all orders in 1/N, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

In this talk I will discuss how to extract the most trascendental piece of the four graviton amplitude in type IIB supergravity on AdS_5 \times S_5 at any loop order, from the dual four point function in N=4 Super Yang Mills. I will describe how to construct this part of the correlator/amplitude and its significance. I will conclude with some open problems and future directions. [Please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

We study quantum field theory in AdS_2 within the framework of Hamiltonian truncation. We start from a solvable theory and we deform the Hamiltonian with an interaction term. We find the spectrum as a function of the coupling, and we aim at connecting the solvable regime with the strongly coupled flat space physics. Hamiltonian truncation in infinite volume presents specific challenges, and special care is needed to recover the physical energy gaps as the cutoff is removed. To this end, we propose a general prescription, we give an argument for its validity and we check it in various examples. [For the link to the Zoom room, please email alejandro.cabo_bizet@kcl.ac.uk].

Purely N=3 SCFTs are naturally strongly coupled, and expected to not have a Lagrangian description manifesting their N=3 supersymmetry. However, these may be reached through a deformation of a theory preserving less supersymmetry. We shall present a strategy to try to conjecture such models, and exemplify it by presenting an N=1 model conjectured to flow to an N=3 SCFT, deformed by a marginal deformation. We shall also discuss and exemplify how such proposals can be tested. [For the Zoom link please email to alejandro.cabo_bizet@kcl.ac.uk]

This is the live session included as part of the LonTI lecture on Conformal blocks in two dimensions. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom.​​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.

Even in weakly coupled QFTs, perturbation theory breaks down when one considers amplitudes with a large number $n$ of legs. The series cleverly organizes as a double expansion in $g^2$ and $g^2n$. I show how the series in $g^2n$ can be fully captured by a semiclassical expansion around a non-trivial solution. Focussing on $U(1)$ symmetric $|\phi|^4$ theory in $4$ and $4-\epsilon$ dimension, I derive explicit and consistent all order results for the anomalous dimension of the complex operator $\phi^n$. When restricting to the Wilson-Fisher fixed point and working on the cylinder, the dominant trajectory is seen to correspond to a superfluid phase for the conserved U(1). This creates a correspondence between, on one side, the spectrum of operators and fusion coefficients and and on the other the spectrum of hydrodynamics modes and their interactions. The results also nicely match Monte Carlo simulations in 3D, compatibly with the stunt of taking $\epsilon=1$. [please email alejandro.cabo_bizet@kcl.ac.uk for the Zoom link]

The AdS/CFT correspondence relates string theory on an Anti de Sitter (AdS) background to a dual conformal field theory (CFT) living on the boundary of AdS. One promising strategy for how to prove the duality is to consider the `tensionless' limit of string theory in which the dual CFT becomes weakly coupled. For the case of string theory on AdS3 we have recently identified a solvable world-sheet description for this tensionless limit. This opens the way towards proving the AdS/CFT correspondence, at least for this specific set-up. Please contact Dionysios Anninos (dionysios.anninos@kcl.ac.uk) for the zoom link.

​​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 ]