In this talk, we delve into the world of spindle and disc solutions dual to 4d SCFTs. Despite extensive studies conducted over the years, certain aspects continue to challenge our understanding. Disc solutions, conjectured to be dual to Argyres-Douglas theories, present a puzzle as at first sight the symmetries do not match across the holographic correspondence. The spindle solutions, on the other hand, completely lack a proper understanding of their dual field theories. This talk aims to shed light on these puzzles, offering a detailed explanation for the breaking of the unwanted symmetry in disc solution. Furthermore, we will clarify various aspects of the spindle solution, contributing to a more profound understanding of the class S origin of the dual SCFTs. As a byproduct, we enlarge the class of holographic surface defects of the (2,0) theory as well as provide a concrete description of a class of locally N=1 preserving punctures.

As is well known, the string spectrum comprises infinitely many states that can collectively be visualized along Regge trajectories of increasing mass and spin. Its massless and lightest levels, as well as certain higher spins including the leading Regge trajectory, have been the focus of past studies. In principle, access to any state is possible, but the traditional methodology is non-covariant and does not immediately lead to irreducible representations of the Wigner little group. In this talk, we will discuss a new and covariant technology of constructing the string spectrum. It is based on the observation that there is a bigger symmetry behind the Virasoro constraints: the symplectic algebra that commutes with the spacetime Lorenz algebra. This enables excavating string states and their interactions by entire trajectories, rather than individually.

A review of the concept of Krylov Complexity(K- Complexity) will be presented. One feature of K-Complexity is that its definition does not involve a tolerance parameter. I will describe some general properties of K-Complexity, its behavior when interpolating among various types of systems: free, strongly integrable and chaotic ones. Finally for a certain low dimensional system in a certain state I will describe an explicit derivation of the geometric bulk dual of K complexity.

In this talk, I present new solutions for type IIB supergravity generated by an infinite family of uplifts from six-dimensional supergravity solutions. After compactification on a circle, I will discuss that these backgrounds are proposed to be holographically dual to confining Quantum Field Theories. In the high energies, field theories will approach the strongly coupled regime of 5d quiver gauge field theories. I also mention some observables like Wilson loops and Entanglement entropy to sketch the properties of the theories.

When do two different looking quantum field theories describe the same physics? This is essentially asking when the quantum field theories are isomorphic. In the case of topological quantum field theories, there are sometimes a way to determine them via topological invariants. For a superconformal field theory, what would be the minimal set of “invariants” to determine when they are isomorphic? I will discuss some approaches to this question in the context of superconformal field theories in four and six dimensions. Utilizing 4d class S theories that also admits 6d (1,0) SCFT origins, I will explain how a certain class of 4d N=2 SCFTs, which a priori look like distinct theories, can be shown to describe the same physics. I will further explain how the 6d (1,0) origin sheds light on the 3d duality.

Higher-order gravities are extensions of General Relativity (GR) which introduce in the classical action terms of higher order in the curvature. These appear naturally in the context of string effective actions, as well as in generic gravitational EFTs. Among the myriads of higher-order gravities one may think of, in this talk I will focus on specific theories whose equations of motion are of second order in derivatives for some particular backgrounds. I will provide many examples of such theories, classification results and argue that a subclass of them actually forms a basis for the space of gravitational EFTs. Afterwards, I will discuss the addition of non-minimal couplings to matter, show that some of these theories possess fully regular black hole solutions and conclude with some holographic applications.

Costello, Witten and Yamazaki proposed a 4d Chern-Simons theory as a unified way to engineer integrable models. In the presence of 'Disorder' defects (for non-ultralocal 2d theories), this correspondence has been established only classically. As a first quantum check, I will derive the matching of 1-loop divergences between the 4d and 2d theories. My assumptions are general and seem to isolate sigma-models among the 2d theories. (Based on 2309.16753)

We study new cohomologies for the BPS operators of the N=4 Yang-Mills theory with SU(2), SU(3) and SU(4) gauge groups. The goal of this programme is to identify the black hole microstates in the dual field theory that are successfully counted by the index to match the Bekenstein-Hawking entropy. We first study the index over non-graviton cohomologies and identify their threshold levels. We present examples of the non-graviton operators in the SU(2) theory and in a subsector of the SU(3) theory that corresponds to the BMN matrix model. We also present an ansatz that can be used to construct these operators. Finally, we discuss non-trivial tower structures and partial no-hair behaviours of quantum black holes.

I will describe a novel class of statistical ensembles we developed for the description of chaotic conformal field theories. These are generalisations of the usual random-matrix type theories used in the description of quantum chaotic many-body systems, and implement the kinematical as well as dynamical constraints of the CFT bootstrap. These novel statistical models take the form of distributions over random matrices and tensors. I will take some time to characterise the individual elements in terms of so-called “approximate CFTs”. Finally, I will discuss the concrete realisation of these ideas for 2D, large-c CFT and point out that the resulting tensor models (subject to reasonable constraints on the spectrum) take the form of an integral over random discrete triangularisation of 3D Euclidean manifolds, governed by the 6j symbols of Virasoro, strongly suggesting a connection to three dimensional quantum gravity.

I this talk I will describe a picture which has emerged over the past few years regarding the statistical interpretation of semiclassical gravity and how this relates to wormholes, averaging and the so-called factorization puzzle, the information paradox, and a combinatorial description of 3d gravity.

We study ensembles of half-BPS bound states of fundamental strings and NS-fivebranes (NS5-F1 states) in the decoupling limit. We revisit a solution corresponding to an ensemble average of these bound states, and find that the appropriate duality frame for describing the near-source structure is the T-dual NS5-P frame in which the fivebranes are generically well-separated; this property results in the applicability of perturbative string theory. The geometry sourced by the typical microstate is not close to that of the black hole that carries the same charges. When members of the ensemble spin with two fixed angular potentials about two orthogonal planes, we find that the ensemble average geometry has an ellipsoidal structure. This contrasts with ring structures obtained when fixing the angular momenta instead of the angular potentials; we trace this difference of ensembles to large fluctuations of the angular momentum in the ensemble of fixed angular potential.

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.