Free strings on backgrounds such as AdS3xS3xT4 and AdS3xS3xS3xS1 can be described by integrable sigma models, which admit a very rich landscape of integrable deformations. In this talk I will focus on TsT, trigonometric and elliptic deformations which preserve some amount of supersymmetries and interpolate between well-known integrable setups. I will present the deformed geometry and check that the S-matrix encoding the scattering of excitations on the string worldsheet is compatible with factorisation.

How well do we understand string theory? As one indicator can be thought of the degree of our understanding of its spectrum. Yet, other than comprising infinitely many physical states of arbitrarily high spin and mass, what does the string spectrum look like? Traditional methodologies can yield its state content on a level-by-level basis, a straightforward procedure which however becomes cumbersome as the level increases. In this seminar, we will discuss a new, covariant and efficient technology with which entire physical trajectories can be excavated. It is based on the observation that the Virasoro constraints in fact encode the generators of a bigger algebra, that is a symplectic algebra, which commutes with the spacetime Lorentz algebra. This enables constructing trajectories deeper inside the spectrum as clones of simpler ones, upon suitably dressing the latter, depending on the depth of the trajectory we aim to reach.

In this talk, we propose that topological order can replace sterile neutrinos as dark matter candidates to cancel the Standard Model global gravitational anomalies. Standard Model (SM) with 15 Weyl fermions per family (lacking the 16th, the sterile right-handed neutrino nuR) suffers from mixed gauge-gravitational anomalies tied to baryon number plus or minus lepton number B+(-)L symmetry. Including nuR per family can cancel these anomalies, but when B+(-)L symmetry is preserved as discrete finite subgroups rather than a continuous U(1), the perturbative local anomalies become nonperturbative global anomalies. We systematically enumerate these gauge-gravitational global anomalies involving discrete B+(-)L that are enhanced from the fermion parity ZF2 to ZF2N. The discreteness of B+(-)L is constrained by multi-fermion deformations beyond-the-SM and the family number Nf. Unlike the free quadratic nuR Majorana mass gap preserving the minimal ZF2, we explore novel scenarios canceling (B+(-)L)-gravitational anomalies while preserving the ZF2N discrete symmetries, featuring 4-dimensional interacting gapped topological orders or gapless sectors (e.g., conformal field theories). We propose symmetric anomalous sectors as quantum dark matter to cancel SM global anomalies. We find the uniqueness of the family number at Nf = 3, such that when the representation of ZF2N from the faithful B+L for baryons at both Nf and N equal to 3 is extended to the faithful Q + NcL for quarks at N = NcNf = 9, this symmetry extension ZNc=3 to ZNcNf =9 to ZNf =3 matches with the topological order dark matter construction. Key implications include: (1) a 5th force mediating between SM and dark matter via discrete B+(-)L gauge fields, (2) dark matter as topological order quantum matter with gapped anyon excitations at ends of extended defects, and (3) Ultra Unification and topological leptogenesis. [Based on arXiv:2502.21319, arXiv:2501.00607, arXiv:2411.05786, arXiv:2012.15860, arXiv:2112.14765, arXiv:2204.08393, arXiv:2302.14862, arXiv:2312.14928].

Recently a formula for free theory (super)block coefficients in many SCFTs was first guessed and then proved https://arxiv.org/abs/2502.14077. I will describe this result and summarise some of the background to it, involving a number of beautiful relations between superblocks, symmetric polynomials, superJacobi polynomials, Heckman Opdam hypergeometric functions, Calogero Sutherland Moser wave functions and Cauchy identities. I will also give a new application to strong coupling N=4 SYM.

Since its discovery by Berkovits 25 years ago, the pure-spinor formulation of the superstring has proven to be a very useful tool in the calculation of scattering amplitudes, both at tree- and loop-level. However, almost all of its applications are confined to the scattering of massless states. Computation of massive string amplitudes is possible in principle, but difficult to perform within the usual pure-spinor prescription. In this talk, I will report progress on computing manifestly super-Poincare invariant amplitudes through an alternative procedure, which does not explicitly involve the pure-spinor variable and should apply equally well to massless and massive external states.

We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several examples and compare them against existing data for the four-point function of the displacement operator. Additionally, we provide a few new predictions that extend the current understanding of these correlators.

I'll briefly review the classical double copy, which maps exact solutions of classical gauge theories like electromagnetism, to solutions of general relativity. We will relate several gravitational objects (including horizons, Penrose limits, and asymptotics, and duals to fluid systems) to their gauge theory analogues.

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.

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.

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.