I will introduce a new 2d gravity/matrix integral duality. The bulk theory is a two-dimensional string theory defined by coupling two copies of Liouville CFT with central charges c = 13 \pm is on the worldsheet. We call this string theory the complex Liouville string. I will argue that the complex Liouville string admits a dual description in terms of a double-scaled two-matrix integral. The string amplitudes, which are the main observables of the complex Liouville string, can be interpreted as cosmological correlators of massive particles, integrated over the metric at future infinity of dS3 to define gauge invariant observables. Furthermore we obtain evidence that the dS3 Gibbons-Hawking entropy can be reproduced exactly by counting the degrees of freedom in the dual matrix integral.

Conformal Field Theory (CFT) represents a class of quantum field theories that have profound applications across various physics domains, from critical phenomena in statistical mechanics to quantum matter, quantum gravity, and string theory. In this talk, I will introduce our recently proposed fuzzy (non-commutative) sphere regularization scheme, a method that addresses and offers a solution to the longstanding need for a non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, conformal defects, and critical gauge theories. Importantly, I will showcase that this scheme is not only potent--revealing a wealth of universal data on 3D CFTs otherwise inaccessible through existing methods--but also efficient, as the necessary computations can be performed on a laptop within an hour. Our innovative scheme not only heralds a new era for the study of CFTs but also hints at a profound interplay between non-commutative geometry and both CFTs and QFTs at large.

Scale symmetry is an important concept in quantum and statistical physics. It arises at fixed points of the renormalisation group, often alongside full conformal symmetry, and implies that theories are massless with correlation functions given by universal numbers. New phenomena arise when scale symmetry is broken spontaneously, leading to a Goldstone boson, the dilaton, and the appearance of a mass scale that is not determined by the fundamental parameters of the theory. In this talk, I discuss scalar, fermionic, and Yukawa theories in three dimensions, each with lines of strongly-coupled conformal fixed points that terminate with spontaneous scale symmetry breaking. Interrelations between models, dualities, and aspects of dilaton physics are worked out from first principles. Further implications for CFTs and model building are indicated.

There are various ways of constructing 5d SCFTs in String Theory; most famously, one can look at geometric engineering in M-theory or webs of 5-branes in type IIB. It is well understood how to translate from one setup to the other in the case where the Calabi-Yau geometry is toric. However, in the type IIB picture, brane manipulations such as Hanany-Witten transitions can lead us beyond the pure toric context; the combinatorial data enconding the system has been dubbed a Generalized Toric Polygon (GTP). In this talk, I will discuss recent progress understanding the geometry of GTPs. A key role is played by the mirror Calabi-Yau, where Hanany-Witten transitions take a very simple form. This allows us to make contact with a mathematical notion of "polytope mutation", and import part of the results in that literature to our physical setup; as an example, we find "mutation invariants" that can prove useful in the classification of 5d SCFTs. Time permitting, I'll also discuss some consequences for the BPS quivers of the 5d theories engineered by GTPs.

I will describe an example of the AdS/CFT correspondence between a 4d N=1 SCFT arising from a mass deformation of N=4 SYM theory and an AdS_5 flux background of type IIB string theory. The SCFT does not admit a weakly coupled description which makes the calculation of its correlation functions challenging. Instead, I will consider a consistent trunctation of the bulk supergravity theory to explicitly compute two- and three-point correlation functions in the planar limit of the CFT. A qualitatively new feature is the presence of unprotected multiplets in the supergravity spectrum. As a non-trivial consistency check of our results, I will show agreement with superconformal Ward identities in the 4d N=1 SCFT. Based on work in progress with Nikolay Bobev.

In 2+1 dimensions quantum particles can exist that are neither bosons nor fermions. Such particles, known as "anyons" have been studied theoretically for over forty years. While there has long been good reason to believe that these particles exist, particularly in fractional quantum Hall systems, it has been frustratingly difficult to perform experiments that probe the properties of these particles --- with many failures over the year. However, just in the last few years, with the maturation of a few new technologies, there have now been several very different but increasingly clear experiments that directly measure the exotic exchange statistics of these particles. I will explain the history of some of these experiments, what they have achieved, and what remains to be done.

Topological manipulations, like gauging a finite symmetry, produce new quantum field theories from known ones. It is natural to ask how effective they are at moving one around theory space. I will sketch an appealing conjectural answer to this question in the context of 2d rational conformal field theories, which leverages ideas and techniques from 3d topological field theory. I will then present a variety of partial results in the direction of this conjecture, and physically motivate the discussion by situating it in broader quantum field theory lore.

The rapid advance in gravitational wave detectors has spurred renewed interest in the two-body problem in general relativity. Two perturbative approaches based on quantum field theory have emerged, one based on scattering amplitudes and the other based on worldlines. We argue that the two approaches are equivalent at an intimate level. By systematic algebraic manipulations through the Schwinger parametrization, the loop integrand in the Kosower-Maybe-O'Connell formalism based on wavepacket scattering becomes identical to the counterpart in the worldline QFT formalism of Mogull et al., as shown explicitly for a simple scalar model as well as electrodynamics at two loops. This makes manifest the cancellations of superclassical divergences and exhibits the emergence of the worldline picture including the classical causality flow.

Physics beyond relativistic invariance and without Lorentz (or Poincare) symmetry and the geometry underlying these non-Lorentzian structures have become very fashionable of late. This is primarily due to the discovery of uses of non-Lorentzian structures in various branches of physics, including condensed matter physics, classical and quantum gravity, fluid dynamics, cosmology, etc. In this talk, I will be talking about one such theory - Carrollian theory, where the Carroll group replaces the Poincare group as the symmetry group of interest. Interestingly, any null hypersurface is a Carroll manifold and the Killing vectors on the null manifold generate Carroll algebra. Historically, Carroll group was first obtained from the Poincare group via a contraction by taking the speed of light going to zero limit as a "degenerate cousin of the Poincare group". I will shed some light on Carrollian fermions, i.e. fermions defined on generic null surfaces. Due to the degenerate nature of the Carroll manifold, there exist two distinct Carroll Clifford algebras and, correspondingly, two different Carroll fermionic theories. I will discuss them in detail. Then, I will show some examples; when the dispersion relation becomes trivial, i.e. energy bands flatten out, there can be a possibility of the emergence of Carroll symmetry.

Four-point correlation functions are observables of significant interest in holographic quantum field theories. In this talk I will describe the computation of a family of four-point correlation functions of operators in short multiplets of 4D N=4 super Yang-Mills theory, by studying the quadratic fluctuations around non-trivial supergravity backgrounds. The supergravity backgrounds are supersymmetric smooth geometries in the family derived by Lin, Lunin and Maldacena. For generic parameters, the supergravity backgrounds are dual to heavy CFT states. However I will also discuss the limit in which the dual CFT states become light single-particle states. The resulting all-light four-point correlators are related by superconformal Ward identities to previously known four-point correlators of half-BPS chiral primary operators. By verifying that the Ward identities are satisfied, we confirm the validity of the supergravity method.

For small values of k and N, this theory describes various experimentally relevant systems in condensed matter, and is also conjectured to be part of a web of non-supersymmetric dualities. We compute the scaling dimensions of monopole operators in a large N and k expansion, which appears to be extremely accurate even down to the smallest values of N and k, and allows us to find dynamical evidence for these dualities and make predictions about the phase transitions. For instance, we combine these estimates with the conformal bootstrap to predict that the notorious Neel-VBS transition (QED3 with 2 scalars) is tricritical, which was recently confirmed by independent lattice simulations. Lastly, we propose a novel phase diagram for QED3 with 2 fermions, including duality with the O(4) Wilson-Fisher fixed point.

Amongst the most fascinating behaviours to arise from Einstein's equations is the onset of chaotic dynamics in the approach to certain cosmological singularities. This was analysed in detail in seminal work by Belinskii, Khalatnikov, Lifshitz (BKL) and others some fifty years ago. A consequence of these results is that the Schwarzschild interior solution near the singularity appears very fine-tuned and should give way for BKL-like dynamics in more generic black holes. In arxiv:2312.11622, we construct a setup that realises the so-called "mixmaster" chaotic dynamics in the interior of an AdS black hole. After reviewing the work of BKL, I will describe our holographic setup and discuss the peculiar symmetries appearing in this problem.

In this talk, I will discuss a novel strategy to fit experimental data using an amplitude ansatz satisfying the constraints of Analyticity, Crossing, Unitarity, and UV completeness. The fit strategy requires both the use of S-matrix Bootstrap methods and non-convex Particle Swarm Optimization (PSO) techniques. As a proof of principle, I will focus on $\pi\pi$ scattering. Using this procedure, I will show how to construct numerically a full-fledged scattering amplitude that fits the available experimental and lattice data, and that features all the known QCD spectrum with quantum numbers $I^G=0^+,1^+$ below 1.4 GeV, plus an additional surprise.

The original singularity theorems of Penrose and Hawking have, in their hypotheses, pointwise energy conditions violated by some classical and all quantum fields. If we want to extend their validity to semiclassical gravity, these conditions have to be replaced by weaker ones. In this talk I will first discuss recent results for singularity theorems with weakened energy conditions, some of which are obeyed by quantum fields. Then I will argue for the need of singularity theorems with worldvolume averaged energy conditions both in the timelike and the null case. For each case I will present progress and open questions.

In the first part of the talk I will recap the black hole thermodynamics of a certain non-supersymmetric asymptotically AdS_5 black hole: I will define its asymptotic charges and associated potentials and show some thermodynamic relations between them. Then I will describe the so-called BPS point, where the black hole is extremal (zero temperature) and supersymmetric. Finally, I will show how to approach the vicinity of the BPS point, without exactly landing on it and discuss the significance of this near-BPS limit and its relation to the Schwarzian mode. In the second part of the talk, I will introduce the holographically dual 4d field theory and describe its basic properties. In particular, I will describe how the supersymmetry breaking (which occurred on the gravity side) can be kept under control on the field theory side. Finally, I will present a preliminary calculation providing a match between the classical gravity partition function and the classical field theory partition function in this thermal setting.

We derive a universal inequality on the unitary 2D CFT partition function with general central charge $c\geqslant 0$, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the bound on the mixed-temperature plane. The infinite iteration of this equation gives the boundary of maximal-validity domain of our inequality. In the $c\to\infty$ limit, with additional assumption of having a sparse spectrum below the scaling dimension $\frac{c}{12}+\varepsilon$ and below the twist $\frac{\alpha c}{12}$ (with $\alpha\in(0,1]$ fixed), our inequality implies that the grand-canonical free energy has universal large-c behavior in the maximal-validity domain, which does not encompass the entire mixed-temperature phase diagram, except in the case of $\alpha = 1$. In particular, we prove the conjecture proposed by Hartman, Keller and Stoica [1405.5137] (the $\alpha=1$ case): the free energy is universal in the large c limit for all $\beta_L\beta_R \neq 4\pi^2$.

Recent developments in the field of integrability include the discovery of higher-dimensional generalised Chern-Simons theories. These theories encode a linear system known as a Lax pair which underpins the integrability of the lower-dimensional theory. We will start with a generous review of these developments before presenting some extensions of this formalism. The applications of these extensions include: integrable deformations (a class of less-symmetric string backgrounds which are nonetheless integrable), stationary axisymmetric general relativity, and gauged WZW models.

Coset symmetry arises in many systems such as Higgs phases of gauge theories and quantum spin liquids. When the coset is quotient by a non-normal subgroup, coset symmetry becomes a non-invertible symmetry. I will discuss properties of coset non-invertible symmetry and its fractionalization using examples in field theories and lattice models, and comment on the dynamical implication. The talk is based on arXiv: 2405.20401 and work in progress with Ryohei Kobayashi and Carolyn Zhang

In recent years, there has been a lot of interest in a generalized notion of symmetry, obtained by relaxing the invertibility constraint and/or allowing symmetry operators to act on submanifolds rather than the full space. The mathematical structure underlying these generalized symmetries is provided by (higher) category theory, but it turns out that in the lattice setting, the abstract categorical formulation can be broken down to concrete tensor network operators that realize these generalized symmetries. In a certain sense, these tensor network operators provide the lattice representation theory of these generalized symmetries. As an application, I will explain how this representation theory provides a systematic, constructive theory for duality transformations on the lattice. Additionally, I will explain how dualities and generalized symmetries can be turned into unitary operators by including an ancillary degree of freedom, turning them into completely positive maps.