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.

The Landau paradigm of phase transitions states that any continuous (second order) phase transition is a symmetry breaking transition. Originally this was formulated for symmetries that form groups, e.g. the critical Ising model is the transition between the $\mathbb{Z}_2$ symmetric and spontaneously broken phases. In recent years a new class of symmetries, called categorical or non-invertible, have emerged in quantum systems -- with impact ranging from high energy and condensed matter physics to mathematics, and quantum computing. I will explain how these symmetries generalize the Landau paradigm and how new phases and phase transitions are predicted, which have potential future experimental implementations in cold atom systems.

Machine learning and related computational methods have become substantially more powerful and are already applied in many areas of science. In the future, they are likely to change scientific research profoundly. In this talk I will be discussing two ways in which machine learning can be helpful in physics: solving differential equations and model building. I will attempt to explain the basic ideas behind these applications and present some recent examples, including inflationary model building, finding string models with certain prescribed properties and computing the masses of fermions from string theory.

In recent years we've expanded our understanding of entanglement in many-body quantum systems; both how it behaves in ground states, and how it grows out-of-equilibrium. Entanglement is very difficult to measure in experiments. But through understanding it better, we've made great progress in classifying quantum phases of matter, and in developing algorithms for efficiently simulating quantum systems. I will review some recent progress in these directions.

Fundamental questions such as emergence of geometry and gravitational dynamics from QFT amplitudes, barring specific examples, remain unanswered at the full stringy level in gauge-gravity duality. In this talk I will discuss recent progress toward a microscopic approach based on the worldline formulation of QFT. In particular, I will consider large-loop quantum corrections in holographic QFTs where internal propagators of Feynman diagrams are characterized by the Schwinger parameters and argue that embedding of string in the holographic coordinate emerges from the continuum limit of these Schwinger parameters at infinite loop limit. I will demonstrate, employing the techniques of Strebel differentials and discrete exterior calculus, how a worldsheet action for a bosonic string embedded in asymptotically AdS space-time could emerge from multi-loop Feynman graphs in a class of bosonic QFTs. I will end with a discussion of possible loopholes in this approach.

Non-invertible symmetries are refined notions of symmetries intensively studied recently. I will show that non-invertible symmetries sometimes lead to a surprising consequence on scattering amplitudes --- a modification of crossing symmetry. I will demonstrate this using example of integrable field theories in 1+1 dimensions although the argument holds more generally; also for non-integrable theories. I will also present the results of S-matrix bootstrap, which constrains the space of physically consistent scattering amplitudes with categorical symmetries.

SymTFTs (or, relatedly, the sandwich construction) have emerged recently as a useful way to think of categorical symmetries. I will give a brief description of this construction, and then review recent work on how to obtain the SymTFT data from geometry in the context of geometric engineering.

This talk will review recent results on the construction of U(1) duality-invariant nonlinear models for gauge (2n-1)-forms in d = 4n dimensions, including $T \bar T$-like flows in the space of such theories. In the four-dimensional case, we will briefly discuss the following U(1) duality-invariant nonlinear systems: (i) models for N-extended superconformal higher-spin multiplets; (ii) the low-energy effective action for N = 4 SYM on its Coulomb branch; and (iii) models for spontaneously broken local N=1 supersymmetry. If time permits, a new formulation for a self-interacting chiral gauge 2n-form in d = 4n + 2 dimensions will be discussed.

It’s been known since the work of Callan and Rubakov that a generic gauge theory harbours a riddle: the scattering of light fermions off heavy magnetic monopoles necessitates exotic outgoing states, seemingly with fractional occupation numbers. I will first explain how we can make sense of these outgoing states in the modern language of generalised symmetries: They are created by operators living at the edge of a topological surface, and in turn correspond to states in a particular twisted Hilbert space. I will then apply this general formalism to the original case of interest, the Standard Model itself, where the resulting states turn out to carry fractionalised baryon and lepton numbers. I will finally discuss various other scenarios, including some that require non-invertible symmetry defects.

Four-dimensional N=2 superconformal field theories give rise, via a cohomological construction that I will review, to associated vertex operator algebras that have been much investigated in the last decade. A curiosity of this construction is that for unitary parent SCFT, the vertex operator algebras so-realised are non-unitary. In this talk I will present the structure on these VOAs that encodes unitarity of the parent theory. Like conventional unitarity, this hidden unitarity imposes strong constraints. I will describe efforts to impose this constraint for Virasoro VOAs (and possibly affine Kac–Moody vertex algebras) leading to (conjectural) classification results for central charges/levels at which these algebras are compatible with four-dimensional unitarity. The talk is based on work in progress with A. Ardehali, M. Lemos, and L. Rastelli.