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.

We consider type IIB string theory with $N$ D3 branes and various configurations of sevenbranes, such that the string coupling $g_s$ is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual either to a to a rank $N$ gauge for any coupling tau, or to non-Lagrangian CFTs such as Argyres-Douglas and Minahan-Nemeschansky theory. We compute the mass deformed sphere free energy F(m) using localization in the case of the Lagrangian theory, and the Seiberg-Witten curve for the non-Lagrangian theories. We show how F(m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS_5 x S^3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. In particular, we compute the log threshold terms for all the theories and the first higher derivative correction F^4 for the Lagrangian theory for finite tau, and find a precise match in the flat space limit in all cases. Finally, we use numerical bootstrap to study the Lagrangian theory at finite N and tau.

Asymptotically-flat spacetimes play a central role in the study of gravitational radiation. They are also the arena which enables to understand the relationship between asymptotic symmetries, soft graviton theorems, and memory effects. While this relationship is well understood at leading order in terms of BMS symmetries and flux-balance laws for the mass and angular momentum, the subleading structure has only begun to be investigated recently. In this talk we will present a study of this subleading structure using the Newman-Penrose formalism. This enables to identify an infinite tower of quasi-conserved charges generating an intriguing algebraic structure.

Recent progress has provided methods to compute and match finite N (supersymmetric) partition functions on both sides of the holographic duality within string and M-theory. An advent that allows for interesting opportunities in the study of quantized strings and branes in curved backgrounds. I will discuss \mathcal{N}=4 SYM, its S-fold cousins, and how localization allows to compute their supersymmetric partition functions analytically as a function of N. We will subsequently discuss some peculiar features of these S-folds; such as their seemingly non-compact conformal manifold, and the fact that their partition functions can be expanded in fluctuating gravitons and D3-branes, very much a-like the giant graviton expansion in \mathcal{N}=4 SYM, even though a clear index interpretation is absent on the QFT side.

I will present a method for deriving the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in AdS(4). This is achieved by analyzing the large-N limit of the spindle index.

Detecting local Non-Gaussianity provides valuable insights into the early universe's particle composition. Interactions between the inflaton and light particles yield distinctive signatures, potentially observable in upcoming surveys. However, addressing IR divergences in light fields on de Sitter spacetimes requires careful treatment. Stochastic inflation offers a solution, but its relationship with perturbative computations remains unclear. In this presentation, we establish a precise connection between perturbation theory and stochastic formalism using the wavefunction formalism. We extend this analysis to multifield inflation models and clarify recent non-perturbative findings from stochastic inflation through their compatibility with perturbation theory calculations.

Topological orders in 2+1 dimensions are captured by modular tensor categories (MTCs). We propose a correspondence that assigns a fusion category to a pair (M,G), where M is a Seifert 3-manifold and G is an ADE Lie group. We conjecture that the fusion category associated to (M,G) is an MTC if and only if M has trivial first homology group with coefficients in the center of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to access the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realizing all MTCs (unitary or non-unitary) with rank at most 5.

We describe a powerful new technique for computing various physical observables in supergravity, without solving any supergravity equations. Applications include gravitational free energies, black hole entropies, and central charges and other CFT quantities of interest in holography. In the talk I will aim to describe the general idea, and give a flavour of some applications.

I will review the theoretical and experimental status in the search of primordial non-Gaussianity, focussing on some recent developments and ideas. In particular I will try to answer the question: what are we going to learn when experiments will be able to probe f_NL ~ 1?

Previous work has given proof and evidence that BPS states in local Calabi-Yau 3-folds can be described and counted by exponential networks on the punctured plane, with the help of a suitable non-abelianization map to the mirror curve. This provides an appealing elementary depiction of moduli of special Lagrangian submanifolds, but so far only a handful of examples have been successfully worked out in detail. In this talk, I will present an explicit correspondence between torus fixed points of the Hilbert scheme of points on ℂ^2⊂ℂ^3 and anomaly free exponential networks attached to the quadratically framed pair of pants. This description realizes an interesting, and seemingly novel, “age decomposition” of linear partitions. We also provide further details about the networks’ perspective on the full D-brane moduli space.

Diverse observations have established the standard cosmological model, known as $\Lambda CDM$. Within this model, the Universe began in a hot dense state filled with tiny primordial density fluctuations. These fluctuations grew as they collapsed under gravity and eventually became the seeds of the galaxies throughout the Universe. A key question is where did these initial perturbations come from? The leading model for their creation, known as inflation, posits that these arose from quantum vacuum fluctuations that were stretched to cosmic scales by a period of exponential expansion of the Universe. Many models predict that this process will leave distinct statistical signatures on the primordial density perturbations. In this talk I will discuss how we can use the spatial distribution of galaxies to search for these early Universe signatures. In particular, I will show how novel analysis methods will allow us to robustly disentangle the primordial information from late-time physics. These approaches will shed new light on aspects from the number of fields present during inflation to the strength of interactions to symmetries of inflation.

I will describe a surprisingly simple representation of a class of integrated correlation functions of four superconformal primaries in the stress tensor multiplet of N=4 supersymmetric Yang-Mills theory with arbitrary simple gauge group, G. I then present exact formulae for these integrated correlators which are manifestly invariant under GNO electro-magnetic duality. For classical gauge groups, G=SU(N), SO(N), USp(2N), In the large-N limit these correlators are interpreted via holography in terms of the low-energy expansion of type IIB superstring amplitudes in AdS_5XS^5 or an orientifold thereof. In this way I recover the SL(2,Z)-invariant BPS interactions, arising in type IIB superstring amplitudes in the flat-space limit. From the asymptotic nature of the 1/N expansion I furthermore reconstruct non-perturbative contributions which holographically correspond to (p,q)-string world-sheet instantons.

QFT at finite temperature can be studied via compactifying the time direction. Placing CFTs on this non-trivial manifold, a subgroup of conformal symmetries is broken. Nonetheless, it is possible to derive broken Ward identities, which provide novel constraints on the theory. These constraints not only systematically reproduce all known results, including an implicit formulation of the generalized Cardy formula, but also relate the thermal energy spectrum with the conformal spectrum. Moreover, novel sum rules for one-point functions of operators are derived. They allow the computation of one-point functions for light operators in terms of zero temperature data, as well as their asymptotic behavior for heavy operators.

It is natural to expect that quantum gravity is not directly relevant at the low energies which experimentally accesible today, since the Planck scale is many orders of magnitude above the electroweak scale. However, mounting evidence coming from String Theory compactifications, general considerations based on black hole evaporation and holography suggest that there are some constraints that must be satisfied by low-energy effective field theories coupled to Einsteinian gravity. These constraints can in principle be used to rule out models at low energies or to connect with observations, an effort dubbed the "Swampland Program". I will review the program, its motivation, and recent advances.

The Symmetry TFT of a quantum field theory is a Topological Field Theory in one dimension more, that describes the structure of the symmetry, its representations, its anomalies, and the possible topological manipulations (gaugings). Until recently only the case of finite symmetries had been addressed. I will present a proposal for the Symmetry TFT of theories with a U(1) symmetry: it is a BF theory with a continuum of topological operators. I will discuss many examples, including chiral anomalies, 2-groups, the non-invertible Q/Z chiral symmetry in 4d with ABJ anomaly, and I will discuss the non-Abelian case as well.

In this talk, we examine a fundamental question posed some time ago by Birkhoff and von Neumann: What are the possible structures of measurement in a theory of Physics? We find striking connections with the conceptual framework of First Order Logic, and apply classification theorems for the automorphism groups of first order relational structures to argue for the uniqueness of Hilbert space as the phase space of a theory with probabilistic transitions between atomic states. We discuss possible applications of these observations to Algebraic Quantum Field Theory.

Recently there has been a renewed interest in the subject of novel types of symmetries, now known as generalized symmetries. An interesting question is what happens to these more general symmetry structures upon compactification to lower dimensions. In this talk, we shall explore this in the context of the compactification of 4d N=1 SCFTs to 2d on spheres.