We propose a novel analytical framework for incompressible Navier-Stokes (NS) turbulence, revealing a duality between classical fluid dynamics and one-dimensional nonlinear dynamics in loop space. This reformulation leads to a universal momentum loop equation, which excludes finite-time blow-ups, establishing a \textit{No Explosion Theorem} for turbulent flows with finite initial noise. Decaying turbulence emerges as a solution to this equation and is interpreted as a solvable string theory with a discrete target space composed of regular star polygons. The derived decay spectrum exhibits excellent agreement with experimental data and direct numerical simulations (DNS), replacing classical Kolmogorov scaling laws with universal functions derived from number theory. These results suggest a deeper mathematical structure underlying turbulence, uniting fluid dynamics, quantum mechanics, and number theory.

In this talk I will present two results of independent interest, the first being more mathematical in nature whereas the second more physical. I will first show that the hierarchy of so-called Higgs branch RG flows between the 6D (1,0) SCFTs known as 'A-type orbi-instantons' is given by the Hasse diagram of certain strata and transverse slices in the (conjectural) double affine Grassmannian of E8. Secondly, by leveraging the partial order naturally defined on this Hasse diagram I will present a proof of the a-theorem for 6D orbi-instanton Higgs branch RG flows, thereby exhausting the list of c-theorems in the even-dimensional (supersymmetric) setting.

Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: "string-ball strings", which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions d≤6 and show that, as the inhomogeneity increases, they approach localized HP balls. We also examine the thermodynamic properties of the different phases in the canonical and microcanonical ensembles. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from the evolution of the black string instability with α' corrections, we propose that, at least in d=4,5, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In d≥6 this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities.

I will discuss a few examples of holographic dual pairs that arise in string theory for quantum theories that are not conformal. In particular, we will focus on Euclidean supersymmetric gauge theories on spheres and compute observables using supergravity and string theory on one side of the duality and supersymmetric localization on the other. This two-pronged approach allows us to study perturbative and non-perturbative corrections to the leading-order holographic result.

I will discuss a few examples of holographic dual pairs that arise in string theory for quantum theories that are not conformal. In particular, we will focus on Euclidean supersymmetric gauge theories on spheres and compute observables using supergravity and string theory on one side of the duality and supersymmetric localization on the other. This two-pronged approach allows us to study perturbative and non-perturbative corrections to the leading-order holographic result.

In this talk I will discuss our recent attempt https://arxiv.org/pdf/2410.23333 of understanding the QCD spectrum using the available experimental data. To do so, we developed a fit strategy that combines the S-matrix Bootstrap with non-convex optimization methods, and applied our algorithm to the case of \pi\pi scattering. The fitted amplitude correctly predicts the low energy ChiPT behavior, the experimental total cross sections at higher energy, and the physical spectrum up to 1.4 GeV. Surprisingly, Bootstrap predicts an additional tetraquark state, not yet observed, and that is being investigated in the decay of the B+ -> pi+ p+ pi- at LHCb.

In the AdS/CFT context, 1/2-BPS asymptotically AdS supergravity solutions can be used to derive holographic 4-point correlators. Beside reproducing known strong-coupling results for the 4-point correlators with single particle states, this approach can be used to derive new 4-point correlators with two single particle and two multiparticle states. I will provide some explicit examples of these correlators with double-particle states both in AdS3 and AdS5. The results can be written in terms of a natural generalisation of the usual D-functions appearing in the 4-point correlators with single particle states.

In the AdS/CFT context, 1/2-BPS asymptotically AdS supergravity solutions can be used to derive holographic 4-point correlators. Beside reproducing known strong-coupling results for the 4-point correlators with single particle states, this approach can be used to derive new 4-point correlators with two single particle and two multiparticle states. I will provide some explicit examples of these correlators with double-particle states both in AdS3 and AdS5. The results can be written in terms of a natural generalisation of the usual D-functions appearing in the 4-point correlators with single particle states.

I will discuss recent work on N=4 SYM with Gaiotto-Witten boundaries, defects and interfaces. This broad class of theories with its high degree of supersymmetry and rich defect dynamics is a natural laboratory for exploring the physics of boundaries and defects, and it contains boundary conformal field theories that underlie string theory realizations of double holography. We will discuss a tight interplay between the holographic duals of these theories and the matrix models arising from supersymmetric localization, defect one-point functions, and large-charge operators.

Gauge (or Yang-Mills) theories are the building blocks of our current physical understanding of the universe. In parallel, string theory is a framework for a consistent quantum description of gravity. Gauge-String duality a.k.a. the AdS/CFT correspondence proposes a remarkable connection between these two very different classes of theories. I will begin by discussing why it is important to arrive at a first principles understanding of the underlying mechanism of this duality relating quantum field theories (QFTs) and string theories (or other theories of gravity). I will then proceed to discuss a very general approach which aims to relate large N QFTs and string theories, starting from free field theories. This corresponds to a tensionless limit of the dual string theory on AdS spacetime. Finally, I will discuss specific cases of this limit for 3d AdS (dual to 2d CFT) and 5d AdS (dual to 4d Super Yang-Mills theory), where one has begun to carry this program through to fruition, going from the string theory to the field theory and vice versa.

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Fusion of two conformal defects in conformal field theory can be understood as an RG flow whose IR fixed point is another conformal defect, with the running scale is set by the separation between the defects. When the separation is small, the system can be described by EFT techniques, in terms of an effective action on the IR defect. In this talk I will discuss the constraints that conformal symmetry imposes on such effective actions, and the implications of this picture for observables such as the cusp anomalous dimension. Joint work with Alexander Radcliffe and Ritam Sinha, arXiv:2406.04561.

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I will present arXiv: 2203.17157 with N. Drukker and G. Sakkas and the paper to appear with N. Drukker and P. Kravchuk. Symmetry-breaking is innate to defects. There is a distinguished set of defect operators that keeps track of the symmetries in the parent conformal field theory broken by the defect insertion, such as the tilt operators and displacement operators. We find identities of such defect operators between their 2-pt functions and integrated 4-pt functions. These identities are derived either from the geometric properties of the defect conformal manifold which is the symmetry-breaking coset, or from the Lie algebra of the corresponding broken symmetry generators. I will demonstrate these integral identities in the case of the 1/2 BPS Maldacena-Wilson loop in N = 4 SYM as an example.

Tidal Love numbers quantify the deformability and dissipative properties of compact gravitating objects. However, even in classical GR, they undergo renormalization group running due to the nonlinearity of gravity. In this talk I will explain some exact results about their running, which can be extracted by matching calculations of scattering amplitudes in black hole perturbation theory and point-particle effective theories. Due to the universality of EFT, the results have applications to the physics of black holes, neutron stars, and even binary systems. For the specific case of black holes, our matching calculation also provides the precise values of both static and dynamical Love numbers in various dimensions.

I will talk about Yang-Mills theory on four dimensional Anti-de Sitter space. The Dirichlet boundary condition cannot exist at arbitrarily large radius because it would give rise to colored asymptotic states in flat space. This implies a deconfinement-confinement transition as the radius is increased. I will show hints on the nature of this transition obtained in 2407.06268 using perturbation theory. The results favor the scenario of merger and annihilation as the most promising candidate for the transition.

We do not understand 95% of our Universe. 63% of this unknown is dark energy (or a cosmological constant), which drives the accelerated expansion of the universe and 27% is dark matter, an additional matter component which clumps together to form large halos around visible galaxies. These two dominating components of the universe have only been observed through their gravitational effects, and both represent the failure of our standard models of particle physics and gravity to explain cosmology from a fundamental physics standpoint. In this talk I will focus on the introduction of new light scalar fields which have been suggested as possible explanations for dark matter and the accelerated expansion of the universe. I will show examples of the unusual phenomenology that can arise in such theories, and explain why properties of macroscopic objects, such as density and compactness, are important in understanding how to detect them. I'll then show how this leads to new opportunities for precision laboratory measurements to shed light on this type of new physics.

In this talk I will discuss how to deal with multi-trace operators, in particular in the context of N=4 Super Yang Mills. I will review their relevance in computing holographic correlators and discuss recent developments on how to treat them.