I will argue that combining old ideas such as dualities and exact results in SUSY QFTs supplemented with recent techniques such as SPT phases and generalised anomalies can shed light on strong coupling dynamics of non-SUSY theories. I will in particular show that non-SUSY gauge theories, which are related to SUSY SCFTs by RG in 5d exhibit phase transitions in the UV which are candidates for non-SUSY fixed points.

In this talk I will introduce the double copy construction that allows us to write gravitational scattering amplitudes as the "square" of gauge theory ones. I will show how the standard construction can be generalized to include massive mediators and how this relationship can also be observed for classical solutions in coordinate space as well as for cohomology class representatives in twistor space. Throughout the talk I will focus on the example of Topologically Massive Theories.

In this talk I will review recent results co-authored with Stefano Negro, Fabio Sailis and István Szécsényi. In this project we have addressed the problem of how to compute correlation functions in integrable quantum field theories perturbed by irrelevant perturbations such as the operator TTbar. It has been known for some time that integrability is preserved under such perturbations even though the S-matrix is modified by a CDD factor. Therefore, it is natural to expect that matrix elements of local fields may be computed by employing the standard form factor program, which was developed for integrable quantum field theories in the 70s. By doing so we have found that the form factors of local and semi-local fields have a universal structure which we have identified. This gives rise to correlation functions with distinct convergence/divergence properties, depending on the sign of the perturbation. In the convergent regime we find that the correlation functions scale as power-laws at short distances, similar to standard integrable quantum field theories, but with powers that are no longer the conformal dimensions of some field. At the heart of our construction is a function called the minimal form factor, whose structure I will discuss in some detail.

We discuss two notions of entanglement of internal degrees of freedom. The first notion is target space entanglement: we show how to define entanglement of matrix degrees of freedom in a gauge invariant manner, and discuss connections to holography. The second notion relates to global symmetries in AdS/CFT settings and relates to an interpretation of Ryu-Takayanagi surfaces which are anchored on the boundary of a subregion on the internal space and smeared in the AdS spatial directions.

We will discuss two classes of line defects in the O(N) critical model at the Wilson-Fisher fixed point. These extended excitations are relevant for condensed matter systems, such as doped quantum antiferromagnets. After reviewing some state-of-the-art analytic bootstrap techniques, we will apply them to compute the correlator of two bulk excitations at first order in the epsilon expansion. From this result we are able to extract an infinite set of defect CFT data.

Scattering amplitudes in strong background fields provide an arena where perturbative and non-perturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strong-field scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from all-order classical observables to constraints on exact solutions. Furthermore, I will discuss how in chiral strong fields, remarkable progress is possible using methods based on twistor theory.

In this talk, I will present a thorough investigation of the Wheeler-de Witt(WdW) equation within the framework of a Reissner-Nordstrom Anti-de Sitter (RN-AdS) black hole background and its relation to holographic renormalization flow. We solve the Wheeler DeWitt equation for the planar Reissner-Nordstrom-AdS black hole in a minisuperspace approximation and construct semiclassical Wheeler DeWitt states from Gaussian wavepackets that are peaked on classical black hole interior solutions. Furthermore, towards the AdS boundary, the Wheeler DeWitt states are used to recover the Lorentzian partition function of the dual theory living on this boundary. This partition function is specified by an energy and a charge. Finally, we show that the Wheeler DeWitt states know about the black hole thermodynamics, recovering the grand canonical thermodynamic potential after an appropriate averaging at the black hole horizon.

The AdS3/CFT2 correspondence is the conjecture that gravity (more specifically superstrings) should be dual to some two-dimensional conformal field theory. Currently, the precise form of this CFT, or its features, are largely unknown. In this blackboard talk, I will review what is know, what is not, and how we are slowly but steadily making progress thanks to techniques from the world of integrable models.

In compactifications over smooth geometrical spaces, closed differential forms can take on a prominent role. For instance, closed forms can represent the geometrical structure of special holonomy manifolds and also fluxes that are present in the compactifications. In this talk, we will describe novel geometrical invariants that arise on manifolds with a distinguished closed form. In particular, we will show that there are natural cohomologies of mapping cone type that in general are dependent on the distinguished closed form. These cohomologies provide another tool to help count the massless scalars that arise in compactifications.

Single field models of inflation capable to produce primordial black holes usually require a significant departure from the standard, perturbative slow-roll regime. In fact, in many of these scenarios, the size of the slow-roll parameter eta becomes larger than one during a short phase of inflationary evolution. In order to develop an analytical control on these systems, I explore the limit of eta large, and promote 1/eta to a small quantity to be used for perturbative expansions. Formulas simplify, and analytic expressions for the two and three point functions of curvature fluctuations are obtained. I will then discuss the behaviour of loop corrections to inflationary observables in this framework

General relativity makes spectacular predictions about our world, predictions which have captured the popular imagination more than any other part of physics: gravitational waves, black holes, spacetime singularities. For the mathematician, however, perhaps the most spectacular thing about these predictions is not their exoticness, but, on the contrary, the fact that they all correspond to well-defined mathematical concepts: Indeed, it was precisely through mathematics that these predictions of general relativity were first discovered—originally to much controversy and objection!—and the qualitative mathematical analysis of the Einstein equations remains one of the most powerful ways to understand the great conceptual questions of the theory. This talk will describe some past contributions of mathematics to general relativity and some of the big open conjectures which mathematics hopes to answer in the future.

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation, together with the spectrum of boundary operators, are sufficient to determine these operators' expectation values uniquely. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.

TBA

TBA

The locality in space of interactions between elementary particles is a key property of our universe. This locality is hardwired into quantum field theoretic descriptions of nature. However, locality and indeed space itself are likely not fundamental concepts. In holographic duality, local interactions on a dynamical spacetime emerge from "large N" matrices where no locality need be manifest in the microscopic Hamiltonian. The emergence of locality from matrix theories is well-established but not well-understood. In recent years it has been appreciated that locally is closely tied up with so-called "area law" entanglement of the microscopic degrees of freedom. I will discuss a particularly robust notion of entanglement in matrix theories that is rooted in an underlying Gauss law constraint and show how simple models of matrix, or 'fuzzy' geometry contain area law entanglement.

I will describe how non-invertible global symmetries act on operators in a quantum field theory. The various possible actions are called generalized charges. This provides a stepping stone for understanding physical applications of non-invertible symmetries, as will be exemplified in the case of Ising symmetry. One of the surprising findings of this endeavor is that there exist new and unexplored generalized charges already for ordinary invertible global symmetries! These generalized charges are described by higher-representations of the symmetry group, generalizing the ordinary charges described by ordinary representations of the symmetry group.

The universe has turned out to be simpler than expected on small and large scales. This encourages us to build unified theories connecting particle physics to the LCDM model. Instead of postulating an ``attractor” phase such as inflation, prior to the hot big bang, we extrapolate the observed universe all the way back to the initial singularity. If the hot plasma in the early universe is perfectly conformal radiation, the singularity is only conformal and one can analytically extend cosmic spacetime and matter through it into a ``mirror” universe on the other side. The universe is then CPT symmetric. We calculate the gravitational entropy for cosmologies with radiation, matter, Lambda and space curvature, finding that thermodynamics favours flat, homogeneous and isotropic universes like ours. To maintain conformal symmetry we include unusual Dim-0 (dimension zero) fields, whose unique physical state is the vacuum. They improve the Standard Model’s (SM’s) coupling to gravity, by cancelling the SM’s vacuum energy and two local “Weyl” anomalies due to gauge fields and fermions. They also cancel the acausal, nonanalytic behaviour introduced into the graviton propagator by loops of SM particles. Cancellation requires (and predicts) precisely 3 generations of SM fermions, each with a RH neutrino, and that the Higgs is composite. One of the RH neutrinos, if stable, is then the simplest-yet proposed viable candidate for the dark matter. Galaxy surveys including EUCLID and LSST will allow precise tests soon. Finally, and most exciting, Dim-0 fields have scale-invariant fluctuations in the vacuum. These source curvature perturbations in the early universe. We recently calculated their power spectrum, ab initio, in terms of Standard Model couplings at the Planck scale. Subject to some theoretical assumptions, the amplitude and spectral tilt closely match the observations, with no free parameters. (See arXiv:2302.00344and references therein).

Over the past few years, it has been shown that, when integrating out the spacetime dependence with a certain integration measure, some four-point correlation functions in N=4 super Yang-Mills (SYM) can be computed exactly. These physical observables are often called integrated correlators, which are functions of Yang-Mills coupling \tau, and transform under S-duality of N=4 SYM. In this talk, I will review some of the recent developments regarding these integrated correlators. In particular, I will discuss the so-called Laplace-difference equations that determine the integrated correlators recursively. I will also present the generating functions of the integrated correlators that resum the ranks of the gauge group and the charges of the operators, from which we will further determine the large-N and large-charge properties of the integrated correctors.

Free or interacting UV fixed points play a key role in the fundamental definition of QFT. In this talk, I give a broad overview of weakly and strongly interacting fixed points in 3d and 4d QFTs including models of particle physics with or without supersymmetry, and fermionic theories. Further, I explain methods and ideas to search for fixed points in 4d quantum gravity. Implications from the viewpoint of CFTs and higher-spin gauge theories through the AdS/CFT conjecture are also discussed.