After reviewing the gravity dual of \(N=6\) Chern-Simons-matter theory, we will analyze the addition of backreacted flavors. We will then construct the corresponding flavored black hole and study the thermodynamic properties of brane probes and of the meson melting transition that they undergo at a certain critical temperature.

Using localization, we solve for the large-\(N\) master field of \(N=2^\ast\) super-Yang-Mills theory and calculate expectation values of large Wilson loops and the free energy. At weak coupling, these observables only receive non-perturbative contributions. The analytic solution holds for a finite range of the 't Hooft coupling and terminates at the point of a large-\(N\) phase transition. We find evidence that as the coupling is further increased the theory undergoes an infinite sequence of similar transitions that accumulate at infinity.

We revisit the existence, background independence and uniqueness of bosonic- and topological string field theory using the machinery of homotopy algebra. In a theory of classical open- and closed strings, the space of inequivalent open string field theories is shown to be isomorphic to the space of classical closed string backgrounds. We then discuss obstructions of these moduli spaces at the quantum level.

We study finite-size corrections of the ${\gamma }_i$-deformed AdS/CFT vacuum energy/anomalous dimension. In particular, we compute the leading (at large volume) and next-to-leading order (NLO) Luescher-like corrections, corresponding to single- and double-wrapping diagrams respectively. On the other hand, we solve to the NLO the twisted Thermodynamic Bethe Ansatz equations describing exactly the ground-state energy of the theory; then we compare the results of the two approaches and find exact agreement. Next, we evaluate explicitly LO and NLO corrections up to six loops at weak coupling.

Finally, I will show some work in progress about the possible conjecture of a Luescher-like formula for the double-wrapping corrections of undeformed excited states energy.

String amplitude computations indicate that the geometry sourced by a bound state of \(D\)-branes differs from the "naive" black hole solution with the same \(D\)-brane charges. We will show how such computations can be applied to the construction of black hole microstates and could shed light on the black hole information paradox.

I will describe the properties of a quantum field theory in compact space subjected to an external magnetic field. In the context of the AdS/CFT correspondence this is realized by introducing flavour branes to the $AdS_5 \times S^5$ geometry in global coordinates. The dual field theory lives on a round three sphere. The theory has a finite Casimir free energy having dissociating effect on the fundamental condensate of the theory. This competes with the pairing effect of the magnetic field leading to an interesting phase structure.

We describe the emergence of nonassociative geometries probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of membranes propagating in the phase space of the target space compactification. Quantization of the membrane sigma-model leads to a proper quantization of the nonassociative background, which we relate to Kontsevich's formalism of global deformation quantization. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras and cochain twist quantization using suitable quasi-Hopf algebras.

The field theory defined on a stack of \(N\) M2-branes is thought to correspond to that first introduced by BLG/ABJM. At large \(N\), an important sector of this theory can be described, holographically, by the \(SO(8)\)-gauged maximal supergravity in four dimensions of de Wit and Nicolai. Since its inception, the latter has been tacitly assumed to be unique. Recently, however, a one-parameter family of \(SO(8)\) gaugings of maximal supergravity has been discovered, the de Wit-Nicolai theory being just a member in this class. I will explain how this overlooked family of \(SO(8)\)-gauged supergravities is deeply related to electric/magnetic duality in four dimensions. I will then discuss some predictions that can be made about the possible family of holographic dual field theories, focusing on the structure of conformal phases and the RG flows between them.

In this talk we review recent progress in the conformal bootstrap program that started with the pioneering work of Rattazzi, Rychkov, Tonni and Vichi (arXiv: 0807.004), mostly focusing on four dimensions. The idea behind this program is to find which values of operator dimensions and operator product expansion coefficients are compatible with the constraints imposed by unitarity and crossing symmetry on four-point correlation functions. In this way one can obtain bounds on these quantities, even if numerically, that must be satisfied in order to have a consistent CFT.

In this talk we will review some recent developments on the quartic matrix model, and its use as a testing ground for ideas of so-called "resurgence". Without going into extreme technical detail we will try to present the relations that were studied and tested, the methods to extract predictions and data in the quartic matrix model (both in the one- and two-cut phases), as well as some natural interpretations of some of the new features. Finally, we will mention some open problems and future directions.

Topological string theory is simple enough to be solved perturbatively, yet it is able to compute amplitudes in string theory and it also enjoys large N dualities. These gauge theory duals, sometimes in the form of matrix models, can be solved past perturbation theory by plugging transseries ansätze into the so-called string equation. Based on the mathematics of resurgence, developed in the 80's by J. Ecalle, this approach has been recently applied with tremendous success to matrix models and their double-scaling limits (Painlevé I, etc). A natural question is if something similar can be done in the stringy side. In this seminar I will show how the holomorphic anomaly equations of Bershadsky-Cecotti-Ooguri-Vafa (BCOV) provide the starting point to derive a master equation which can be solved with a transseries ansatz. I will review the perturbative sector of the solutions, its structure and how it generalizes for higher instanton sectors. Some resurgence in the guise of large-order behavior of the perturbative sector will be used to derive the holomorphicity of the instanton actions that control the asymptotics of the perturbative sector. This work will appear shortly in a paper together with J.D. Edelstein, R. Schiappa and M. Vonk.

Anti-de Sitter (AdS) spacetime is linearly stable, but non-linearly unstable to a weak gravitational turbulent instability. Regardless of how weak the initial scalar or gravitational perturbation of AdS is, this instability forces the system to transfer energy from low to high frequency modes. This energy cascade is similar to what happens with the familiar process of turbulence. In a full time evolution, the scalar instability leads to the formation of a black hole and a similar endpoint is conjectured for the turbulent gravitational instability. In the context of the gravity/gauge theory correspondence, this gravitational instability of AdS provides a holographic description of quantum turbulence in the dual field theory.

The hypermultiplet moduli space \(M_H\) in type II string theories compactified on a Calabi-Yau threefold \(X\) is largely constrained by supersymmetry (which demands quaternion-Kählerity), S-duality (which requires an isometric action of \(SL(2, \mathbb{Z})\)) and regularity. Mathematically, \(M_H\) ought to encode all generalized Donaldson-Thomas invariants on \(X\) consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on \(M_H\), or rather the exact complex contact structure on its twistor space.

We consider extremal solutions in four-dimensional \(N=2\) gauged supergravity. The main focus is on solutions for which no \(\operatorname{AdS}_2 \times \mathbb{R}^2\) horizon can be found, but that instead possess pathological near-horizon geometries. By adding quantum corrections, we show that a regular horizon develops; furthermore we show that these horizons correspond to black brane solutions with \(\operatorname{AdS}_4\) asymptotics. Finally we develop the appropriate entropy function formalism to incorporate the effect of higher-curvature corrections on similar solutions.

We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field. We show that the partition function depends only on this vector field, giving an explicit expression in terms of the double sine function. In the large \(N\) limit our formula agrees with a recently discovered two-parameter family of dual supergravity solutions. We also explain how our results may be applied to prove vortex-antivortex factorization. Finally, we comment on the extension of our results to three-manifolds with non-trivial fundamental group.

We review recent developments in duality symmetric string theory. We begin with the world sheet doubled formalism which describes strings in an extended space time with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an \(E_{n(n)}\) U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extend space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.

The microscopic description of the 4 dimensional supersymmetric (or BPS) black holes in flat space has already been well understood via the AdS/CFT correspondence on the black hole horizon. In this talk I address the similar problem of finding the dual description for BPS black holes in \(AdS_4\). The gravity picture of a flow between asymptotic \(AdS_4\) and \(AdS_2 \times S^2\) on the horizon can be understood as a renormalization group (RG) flow between a 3d and a 1d superconformal field theory. I discuss in some detail both the supergravity and the field theory side, providing evidence for their precise match. At the end I present a proposal for the 1d CFT states that make up the black hole entropy.