I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory

The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In the first part of the talk, I will explain Tseytlin’s prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and α′. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. In the second part of the talk, I will explain the underlying conceptual structure of the Susskind and Uglum black hole entropy argument. There I will show how the classical (tree-level) effective action and entropy S = A/4G_N can be calculated from the sphere diagrams. Time permitting, I will also discuss ongoing work for deriving the holographic entanglement entropy (the RT formula) in AdS3/CFT2. I will end with mentioning some important insights into how the ER=EPR hypothesis can be implemented using tachyon condensation on orbifolds in string theory.

After reviewing different aspects of thermalization and chaos in holographic quantum systems, I will argue that universal aspects can be captured using an effective field theory framework that shares similarities with hydrodynamics. Focusing on the quantum butterfly effect, I will explain how to develop a simple effective theory of the 'scramblon' from path integral considerations. I will also discuss applications of this formalism to shockwave scattering in black hole backgrounds in AdS/CFT.

Line defects play an important role in our understanding of QFTs, explaining interesting phenomena in both condensed matter physics and high-energy theories, and giving access to new data and observables. I will discuss recent work in which we explore 1d conformal line defects with an additional O(2) symmetry using the numerical bootstrap. The starting point is an agnostic approach, where we perfom a systematic bootstrap study of correlation functions between two canonical defect operators: the displacement and the tilt. We then move on to study two specific defects: a monodromy line defect and a localized magnetic field line defect. I will highlight the results of the latter one, where we found a series of intriguing cusps which we investigate.

According to the correspondence principle, classical physics emerges in the limit of large quantum numbers. We examine two examples of the semiclassical description of conformal field theory data: large spin impurities in the free triplet scalar field theory and large charge Wilson lines in QED. By simultaneously taking the coupling to zero and quantum numbers to infinity, we can connect the microscopic to the emergent classical description smoothly.

The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood. In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.

I will discuss the two-dimensional O(n) model for a continuous range of n. It can be defined non-perturbatively for any n as an infrared limit of certain lattice loop models, which in the IR give rise to two families of CFTs. For n<2 these CFTs are logarithmic, while for n>2 they are also complex. For n<2 the RG flow to the fixed points violates the straightforward notion of naturalness and appears tuned.

I will present an ongoing work on an integrable long-range deformation of the XXZ spin chain which can also be seen as a quantum deformation of the Haldane-Shastry model. At generic values for the deformation parameter, the model possess quantum affine symmetry, but when q is root of unity we expect extra symmetries to occur. We are studying the case q=i, which in the nearest neighbour case is solvable by the Jordan-Wigner transformation. The long-range case is also reducible to a fermionic long-range model. I will discuss the main characteristics of the model, which are very different for the even and odd number of sites.

Boundary critical behaviours of systems at bulk criticality have been studied by condensed matter physicists for decades, in the beginning mostly theoretically, then also experimentally. These studies have revealed that the field of boundary critical phenomena is quite rich. For any universality class of bulk critical behaviour usually several distinct universality classes of boundary critical behaviour exist. To elucidate this, we introduce appropriate lattice models and map them onto boundary field theories describing their scale and conformal invariance on large scales. We show that this mapping can be subtle in some cases. We discuss the role and difference of boundary conditions of the field theories on mesoscopic and large scales, to what extent they are characteristic of --- and hence may be used to identify --- the distinct boundary universality classes. Finally, we explain the characteristic near-boundary asymptotic behaviours they exhibit and mention some open problems.

Fracton phases are characterized by their elementary excitations having restricted mobility, and have recently been of relevance in several subjects, from quantum information to thermalization, from gravity to elasticity. In the context of hydrodynamics it has been shown theoretically, and confirmed experimentally, that such restricted mobility leads to novel emergent scaling laws. In this talk, I will introduce a framework to describe the hydrodynamics of fractons and predict such scaling laws, with particular focus on systems with conserved dipole and momentum. This hydrodynamics turns out to have rather exotic properties, owing to the fact that dipole conservation leads to a non-trivial extension of spacetime symmetries. After developing an effective theory approach that allows accounting for fluctuations, I will show that such theory contains relevant nonlinearities that lead to the emergence of stochastic non-Gaussian universality classes, even in three spatial dimensions, thus constituting a breakdown of its local hydrodynamic description.

The Schwinger model is one of the simplest gauge theories, yet it is only solvable in the massless case. In order to obtain numerical results, the Kogut-Susskind lattice approach with staggered fermions is regularly used. I will show that, contrary to what it was believed, the lattice mass and the continuum mass are actually not the same, but they are related by a mass shift. This can be understood by considering the (anomalous) chiral symmetry in the massless case, and has the advantage of greatly improving convergence of the numerics. I will comment on the charge-q Schwinger model as well as the multiflavor Schwinger model.

In conformal field theory, the lightcone bootstrap is an analytic approach to solving the crossing equations of correlation functions. The blocks, namely the kinematical constituents of a crossing equation, must be computed near lightcone singularities and resumed. At four points, this culminates in the universal dynamics of a double-twist operator at large spin. While extensions to higher points have been recently studied, further progress has been hampered by our limited knowledge of the blocks. In this talk, I will review the first applications of conformal block integrability to the multipoint lightcone bootstrap, focusing on scalar five point functions for concrete expressions. First, starting from a Gaudin model, I will review the construction of an integrable system that determines blocks via differential equations and a boundary condition. These differential equations, and by extension the crossing equations, can be explicitly solved in lightcone limits. Finally, after summarizing the old and new results we obtain at five points, I will comment on what this may entail for universal triple-twist data in six point functions. This is based on my thesis work, as well as an upcoming paper with Lorenzo Quintavalle, Apratim Kaviraj and Volker Schomerus.

The Quantum Spectral Curve (QSC) is a powerful integrability-based method capable of computing the spectrum of planar N=4 SYM. It has also been generalised in many directions, for example to cusped Wilson lines and various deformations. The success of the QSC motivates trying to extend the formalism beyond N=4 to other theories. This requires the study of the underlying structure of the QSC, a so called analytic Q-system. To construct an analytic Q-system it is necessary to specify both its algebraic structure, usually encoded into QQ-relations, and its analytic properties. I will talk about recent work to study Q-systems beyond the ones relevant for N=4, discussing both their algebraic and analytic properties. In particular I will discuss the recent conjecture of a QSC for AdS3/CFT2 which non-trivially couples two different Q-systems. While the curve shares many features with the N=4 QSC it also offers new surprises and challenges. If this new curve can be brought under full control and further tested many interesting applications and generalisations are within reach.

Dissipative relativistic hydrodynamics is expected to describe the late times, thermalised behaviour of strongly coupled fluids such as a strongly coupled super Yang-Mills plasma. These systems are then accurately described by a hydrodynamic series expansion in small gradients. Surprisingly, this hydrodynamic expansion is accurate even when the systems are still quite anisotropic: the non-hydrodynamic modes governing the non-equilibrium behaviour at very early-times become exponentially close to the hydrodynamic solution in an early process called hydrodynamization. This early success is intimately related with the fact that the hydrodynamic expansion is asymptotic. The theory of transseries and resurgence explicitly shows how the non hydrodynamic modes are in fact encoded in this late-time expansion. In this talk we will focus on a MIS-type model and use exponentially accurate summations of the the late-time resurgent transseries to recover the behaviour of the fluid before hydrodynamisation, and effectively match it to any given initial non-equilibrium condition. We will further show that such summations can provide analytic predictions beyond the late time regime.

I will speak about my recent work with Zechuan Zheng where we study the SU(Nc) lattice Yang-Mills theory in the t Hooft limit Nc -> infinity, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on maximal length of wilson loops, and the positivity conditions on certain correlation matrices. We thus obtain rigorous upper and lower bounds on plaquette average at various couplings. The results are quickly improving with the increase of the cutoff L. In particular, for D=4 and L=16, the upper bound data in the most interesting weak coupling phase are not far from the Monte-Carlo results and they reproduce well the 3-loop perturbation theory. We also attempt to extract the information about the gluon condensate from this data. Our results suggest that bootstrap can provide a tangible alternative to, so far uncontested, Monte Carlo approach. I will also mention our bootstrap results for an "unsolvable" two-matrix model in the large N limit, where this method appears to be superior in efficiency over Monte Carlo.

The insertion of local operators along a straight Maldacena Wilson line in planar N=4 super Yang Mills defines a defect supersymmetric conformal field theory in one dimension. This is a simple but interesting setup where one can combine field theory techniques such as bootstrap, integrability and localization, aiming at a full solution of a non-trivial quantum mechanical system. I will adopt a bootstrap approach and study correlation functions of local operators for large t Hooft coupling, where the system is dual to an open superstring in $AdS_5 \times S^5$. I will present results for the four-point function of the displacement multiplet of the 1d defect CFT corresponding to three-loop diagrams in AdS, which are obtained using a suitable position-space ansatz and after considering a large system of mixed correlators. The problem is made particularly hard by the large degeneracy of operators at strong coupling, which we solve by taking into account four-point functions with external unprotected operators. The simple 1d kinematics is an ideal toy model for bootstrap techniques of interest for higher-dimensional cases as well. The seminar will be based on published as well as ongoing work with Carlo Meneghelli (see arxiv:2103.10440).

The operator product expansion of massless celestial primary operators of arbitrary spin is investigated. Poincaré symmetry is found to imply a set of recursion relations on the operator product expansion coefficients of the leading singular terms at tree-level in a holomorphic limit. The symmetry constraints are solved by an Euler beta function with arguments that depend simply on the right-moving conformal weights of the operators in the product. These symmetry-derived coefficients are shown not only to match precisely those arising from momentum-space tree-level collinear limits, but also to obey an infinite number of additional symmetry transformations that respect the algebra of w(1+infinity). In tree-level minimally-coupled gravitational theories, celestial currents are constructed from light transforms of conformally soft gravitons and found to generate the action of w(1+infinity) on arbitrary massless celestial primaries. Results include operator product expansion coefficients for fermions as well as those arising from higher-derivative non-minimal couplings of gluons and gravitons.

We present a new family of exact four-dimensional Taub-NUT spacetimes in Einstein-Λ theory supplemented with a conformally coupled scalar field exhibiting a power-counting super-renormalizable potential. Our configurations are constructed in the following manner: A solution of a conformally coupled theory with a conformal potential, henceforth the seed (gμν,φ), is transformed by the action of a specific change of frame in addition with a simultaneous shift of the seed scalar field. The conformal factor of the transformation and the shift are both affine functions of the original scalar φ. The new configuration, (ḡμν , φ̄), solves the field equations of a conformally coupled theory with the extended aforementioned super-renormalizable potential, this under the presence of an effective cosmological constant. The new spectrum of solutions is notoriously enhanced with respect to the original seed containing regular black holes, wormholes, and bouncing cosmologies. We highlight the existence of two types of exact black bounces given by de Sitter and anti-de Sitter geometries that transit across three different configurations each. The de Sitter geometries transit from a regular black hole with event and cosmological horizons to a bouncing cosmology that connects two de Sitter Universes with different values of the asymptotic cosmological constant. An intermediate phase, which might be represented by two different configurations, takes place. These configurations are given by a de Sitter wormhole or by a bouncing cosmology that connects two de Sitter Universes, both under the presence of a cosmological horizon. On the other hand, the anti-de Sitter geometries transit from a regular black hole with inner and event horizons to a wormhole that connects two asymptotic boundaries with different constant curvatures. The intermediate phase is given in this case by an anti-de Sitter regular black hole with a single event horizon. This regular black hole might appear in two different configurations. As a regular anti-de Sitter black hole inside of an anti-de Sitter wormhole or as an anti-de Sitter regular black hole with a cosmological bounce in its interior. All these geometries are shown to be smoothly connected by the mass parameter only. Other standard stationary black holes, bouncing cosmologies and wormholes are also identified.

General Relativity in asymptotically flat spacetimes gives rise to an infinite number of symmetries which form the celebrated BMS group comprising superrotations and supertranslations. These symmetries are closely related to soft theorems of gravitational scattering amplitudes. Recently it was shown that supertranslations and superrotations are only the lowest levels of a whole tower of symmetries of tree level gravitational scattering amplitudes that form a w_{1+\infty} algebra. The fate of this symmetry once loop effects are taken into account is currently unknown. In this talk I will review the emergence of this symmetry algebra based on the celestial CFT program and argue that the w_{1+\infty} algebra persists quantum corrections in self-dual gravity. This talk is based on 2111.10392 with A.Ball, S. Narayanan, and A. Strominger.