Four-dimensional gauge theories can flow in the IR to non-trivial CFTs. By employing Borel resummation techniques both to the ordinary perturbative series and to the Banks-Zaks conformal expansion, we first analyze the conformal window of QCD and find substantial evidence that QCD with n_f=12 flavours flows in the IR to a CFT. We then study UV fixed points for SU(n_c) gauge theories with fundamental fermion matter in 4+2epsilon dimensions. Using resummation techniques similar to those used in the 4d QCD case, we provide evidence for the existence of non-supersymmetric CFTs in d=5 space-time dimensions in a certain range of colors and flavours.

Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior and study it at arbitrarily late times for black holes in various models of two-dimensional gravity. Because of a novel universal cancellation between the contributions of the semi-classical black hole spectrum and some of its non-perturbative corrections, we find that, after a linear growth at early times, the length of the interior saturates at a time, and towards a value, that is exponentially large in the entropy of the black hole. This provides a non-perturbative confirmation of the complexity equals volume proposal since complexity is also expected to plateau at the same value and at the same time.

The aim of this talk is to give a mathematical definition of the superconformal index of 3d supersymmetric gauge theories. This can be computed exactly using supersymmetric localisation, leading to an explicit contour integral formula involving infinite q-Pochammer symbols. I will explain how this may be understood as the Witten index of a supersymmetric quantum mechanics, or index of a twisted Dirac operator on a certain infinite-dimensional space closely related to one introduced by Braverman-Finkelberg-Nakajima.

In this talk, I will discuss AdS super gluon scattering amplitudes in various spacetime dimensions. These amplitudes are dual to correlation functions in a variety of non-maximally supersymmetric CFTs, such as the 6d E-string theory, 5d Seiberg exceptional theories, etc. I will introduce a powerful method based on symmetries and consistency conditions, and show that it fixes all the infinitely many four-point amplitudes at tree level. I will also point out many interesting properties and structures of these amplitudes, which include the flat space limit, Parisi-Sourlas-like dimensional reduction, hidden conformal symmetry, and a color-kinematic duality in AdS. Along the way, I will also review some earlier progress and the relation with this work. I will conclude with a brief discussion of various open problems. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. The agreement with experiments is good in many cases, e.g. the 3D Ising model, but disagreements between theory and experiment that have remained unresolved for decades also exist. This indicates that our understanding of critical phenomena may be incomplete. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of CFTs. In this talk we will review the numerical conformal bootstrap method and discuss potential resolutions it has suggested for unsettled questions pertaining to critical phenomena in frustrated magnets and structural phase transitions. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

This talk will discuss higher-derivative corrections to four-dimensional gauged supergravity and their holographic implications. After briefly reviewing the construction of N=2 supersymmetric higher-derivative invariants, I will introduce a four-derivative action parameterized by two real constants. In this theory, one can show that the two-derivative solutions are not modified by the higher-derivative corrections. This fact has important consequences for the regularized on-shell action, as well as for the thermodynamics of black hole solutions. Moreover, in the context of AdS4/CFT3 holography, I will explain how our results lead to an explicit expression for subleading corrections in the large-N expansion of supersymmetric partition functions of a large class of dual field theories arising from M2 and M5 branes. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

We review the recent progress regarding current operators in integrable models, focusing especially on integrable spin chains. These operators describe the flow of the conserved charges, and they are important for the construction of Generalized Hydrodynamics. They are also connected to long range deformations and TTbar-like deformations of the spin chains, and also to the theory of factorized correlation functions. We argue that these operators are very special, because their mean values can be computed relatively easily even in nested spin chains. This is rather unique because mean values in nested models are rather difficult to compute for generic operators. We review these various connections and also show how to construct current operators using the Quantum Inverse Scattering Approach, the canonical framework developed by the Leningrad school. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

I will discuss the tools we are developing to calculate correlation functions of primordial inflationary perturbations. In this talk, we will focus on the limit where gravitational excitations are neglected and the cosmological spacetime is assumed to be exactly de Sitter. Even in this simplifying limit, which corresponds to a Quantum Field Theory on a de Sitter background, very few examples of explicit analytic calculations exist and little is known about basic properties of the correlators. I will show that for any dS QFT there exists a theory formulated in a Euclidean Anti-de SItter space and which reproduces all the correlation functions. This leads to major technical simplifications and allows to demonstrate various analytic properties of the cosmological observables. Understanding of these properties has both phenomenological applications in inflation, as well as provides some hints about more fundamental description for cosmological spacetimes. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

In this talk I will discuss boundary RG flows for a 4d free scalar field coupled to large N vector models on a 3d boundary. These RG flows connect decoupled fixed points with the free and the critical vector model on the boundary, and they enjoy strong-weak dualities. I will also consider adding gauge fields to the setup. [Please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

An important open question in black hole thermodynamics is about the existence of a "mass gap" between an extremal black hole and the lightest near-extremal state within a sector of fixed charge. In this talk, I will discuss how to reliably compute the partition function of 4d Reissner-Nordstrom near-extremal black holes at temperature scales comparable to the conjectured gap. I will show that the density of states at fixed charge does not exhibit a gap in the simplest gravitational non-supersymmetric theories; rather, at the expected gap energy scale, we see a continuum of states whose meaning we will extensively discuss. Finally, I will present a similar computation for nearly-BPS black holes in 4d N=2 supergravity. As opposed to their non-supersymmetric counterparts, such black holes do in fact exhibit a gap consistent with various string theory predictions. [please email alejandro.cabo_bizet@kcl.ac.uk for the zoom link]

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.