I will review the basic story behind the black hole/string correspondence, its advantages, and its limits. I will then summarize some recent progress on this topic and go over several possible open directions.

In this talk, I will briefly describe two of our recent pieces of work on the physics of the J1-J2 Heisenberg spin chain, a one-dimensional array of quantum spins coupled by first- and second-neighbour exchange interactions. The first piece of work [1] concerns the case where J1 and J2 are both antiferromagnetic: in this case there is a phase transition from a Luttinger liquid to a valence bond solid as In this talk, I will briefly describe two of our recent pieces of work on the physics of the J1-J2 Heisenberg spin chain, a one-dimensional array of quantum spins coupled by first- and second-neighbour exchange interactions. The first piece of work [1] concerns the case where J1 and J2 are both antiferromagnetic: in this case there is a phase transition from a Luttinger liquid to a valence bond solid as J2/J1 In this talk, I will briefly describe two of our recent pieces of work on the physics of the J1-J2 Heisenberg spin chain, a one-dimensional array of quantum spins coupled by fi rst- and second-neighbour exchange interactions. The first piece of work [1] concerns the case where J1 and J2 are both antiferromagnetic: in this case there is a phase transition from a Luttinger liquid to a valence bond solid as J2/J1 is increased, and we provide a novel direct method to derive the field theory that describes the critical point between these two phases. The second piece [2] concerns the case where J1 is antiferromagnetic but J2 is strongly ferromagnetic: counter-intuitively, there is a transition in this case as well, but this time of a "liquid-to-liquid" type. We present a field-theory description of it, and an analogue system of three coupled chains that helps to illustrate the physics. [1] F. Azad, A. J. McRoberts, CAH, and A. G. Green, "Generalized Haldane map from the matrix product state path integral to the critical theory of the J1-J2 chain," Phys. Rev. Research 7, L012037 (2025). [2] A. J. McRoberts, CAH, and A. G. Green, "Transition between critical antiferromagnetic phases in the J1-J2 spin chain," arXiv:2411.08095v2 (2025).

A recently introduced class of 5d superconformal field theories (SCFTs), dubbed 5d conformal matter (CM) in reference to the well known 6d CM theories, is constructed in M-theory on Calabi-Yau threefolds (CY3s) which can be viewed as intersecting ADE singularities. I will address the classification of these theories - based on the weight lattice of ADE algebras - which fall into three classes: Atoms, Molecules, and so called Hybrids. I will show how these three types are distinguished by their geometric construction. Further we will explore the brane constructions dual to the CY3s where possible, the quantum Higgs branch of the 5d CM theories, and the circle reduction to 4 dimensions.

Quantum theories of gravity are generally expected to have some degree of nonlocality, with familiar local physics emerging only in a particular limit. Perturbative quantum gravity around backgrounds with isometries and compact Cauchy slices provides an interesting laboratory in which this emergence can be explored. In this context, the remaining isometries are gauge symmetries and, as a result, gauge-invariant observables cannot be localized. Instead, local physics can arise only through certain relational constructions. In this talk, we explore such issues for perturbative quantum gravity around de Sitter space. In particular, we describe a class of gauge-invariant observables which, under appropriate conditions, provide good approximations to certain algebras of local fields. Our results suggest that, near any minimal hypersphere in dS, this approximation can be accurate only over regions in which the corresponding global time coordinate spans an interval of order ln G^(-1). In contrast, however, we find that the approximation can be accurate over arbitrarily large regions of global dS so long as those regions are located far to the future or past of such a minimal sphere. This talk is based on the paper arXiv:2410.00111 with Donald Marolf, Xuyang Yu, and Ying Zhao.

We obtain the Hawking spectrum by exponentiating a series of Feynman diagrams describing a scalar field scattering through a collapse background. Our approach is rooted in semiclassical methods of scattering amplitudes which have recently been developed for application to gravitational-wave physics. The diagrams we encounter do not compute a standard amplitude, but rather an in-in generalisation of an amplitude which is closely connected to the Bogoliubov coefficients. We also compute the subdominant one-loop correction in our perturbative approach, analogous to the triangle correction to Schwarzschild scattering. This term can be interpreted as a finite-size correction sensitive to the radius of the black hole.

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.