Iberian Strings Meetings 

With a focus in their CFT interpretation, in this talk we study $AdS_3$ solutions in massive type IIA supergravity and $AdS_2$ solutions in type IIB supergravity. From the geometry, we engineer the dual CFT with well known tools and propose a duality with a precise family of quivers. Additionally, we compute field theory and holographic central charges showing a clean matching in both descriptions.

Review lecture on Geometric Extremization for AdS/CFT and Black Hole Entropy.

Certain physical properties of SCFTs with an abelian R-symmetry are determined by the R-symmetry. Furthermore, the R-symmetry can be obtained by an extremization principle. If the SCFT has a holographic dual there is a geometric version of the extremization principle which is a powerful tool in identifying and studying the dual SCFT as well as being of intrinsic geometric interest.

We focus on supersymmetric $AdS_3 \times Y^7$ solutions of type IIB supergravity dual to $N=(0,2)$ SCFTs in $d=2$, as well as $AdS_2 \times Y^9$ solutions of $D=11$ supergravity dual to $N=2$ supersymmetric QMs, some of which arise as the near horizon limit of supersymmetric, charged black hole solutions in $AdS_4$. Our results allow us to identify infinite classes of $d=2$ SCFTs and susy QMs that are obtained by by wrapping higher dimensional SCFTs on Riemann surfaces. For the latter case our results provide a microstate counting of the entropy of a class of supersymmetric black holes in $AdS_4$.

Outreach colloquium on the discovery of a supermassive compact object at the centre of our galaxy.

Black Holes are among the most mysterious objects in the Universe. They are so massive and compact that nothing - not even light - can escape their gravity. The 2020 Nobel Prize in Physics was awarded to Roger Penrose for showing that these exotic objects are a direct consequence of Einstein's general theory of relativity, and to Reinhard Genzel and Andrea Ghez for the discovery of such a monster in the center of our Galaxy. Our presentation will portrait the 40 year journey from the first indications to the overwhelming observational evidence for a extremely heavy and compact object in the Galactic Center, for which a supermassive black hole is the only known explanation. Using the world's largest telescopes and most advanced optics technology, astronomers can now follow the stars orbiting the central object, precisely measure its mass, and detect the stunning effects of general relativity. In our talk we will present both the spectacular observations and the technology behind.

I will show that there is a wide class of integrable sigma models, which includes $CP^{n-1}$, Grassmannian, flag manifold models, that are equivalent to bosonic (and mixed bosonic/fermionic) chiral Gross-Neveu models. The established equivalence allows to effortlessly construct trigonometric/elliptic deformations, provides a new look on the supersymmetric theory and on the cancellation of anomalies in the integrability charges. Using this formalism, we develop criteria for constructing quantum integrable models related to quiver varieties. Based on arXiv:2006.14124 and arXiv:2009.04608

I will present the $T \bar{T}$-perturbed version of $q$-deformed two-dimensional Yang-Mills theory. I will show that the operator $T \bar{T}$ spoils the factorization of the partition function into chiral/anti-chiral sectors. On the other hand, it preserves a large $N$ third order phase transition, although modifying the phase diagram. Implications for the entanglement entropy at large $N$ will be discussed as well. I will conclude with comments on the potential applications of these results to the Bethe/gauge correspondence and to four-dimensional supersymmetric theories.

Based on joint work with Richard J. Szabo and Miguel Tierz, arXiv:2009.00657

The AdS-CFT correspondence is a very powerful tool that allows us to compute field theory observables from a gravity dual. One of the hurdles of this duality is to obtain a dual geometry from certain QFTs such as QCD. In the past few years, some efforts have been made to use deep learning techniques to generate the dual geometry from some known data in the QFT. In particular, Hashimoto et al. were able to propose some geometries dual to QCD using this kind of techniques. The aim of our work is to reproduce the metric of a black hole from the $q \bar q$ potential in a deconfined phase. In particular, we compare the potential generated by a given geometry and compare it to the QFT results in order to train the net.

Review lecture on Machine learning in field theory and string theory.

Backgrounds of perturbative string theory are known to enjoy various duality symmetries, relating different points in the space of vacua. Among these are the perturbative T-duality symmetries, relating backgrounds with a certain amount of space-time isometries to dual field configurations. Depending on the algebra of Noether currents one finds abelian, non-abelian or Poisson-Lie T-duality symmetries. Non-abelian U-duality symmetry is a generalisation of Poisson-Lie T-duality transformation to the case of 11-dimensional backgrounds, where the string becomes non-perturbative. This is based on the concept of exceptional Drinfeld double, which is a generalisation of the classical Drinfeld double Lie algebra to Leibniz algebras. In this talk this algebraic construction is reviewed, a generalisation of Buscher rules to the case of non-abelian U-duality of group manifold backgrounds is described and a set of examples is presented. The related concept of tri-vector and six-vector deformations is also discussed and the corresponding generalisation of the classical Yang-Baxter equation governing integrable bi-vector deformations is overviewed.

In this talk, I describe recent progress in understanding the background field dynamics of the non-relativistic string theory pioneered by Gomis and Ooguri. It is well-known that the underlying string sigma model can be obtained via a limiting procedure — based on a crucial cancellation of infinities — from the relativistic Polyakov model. I show that a similar, subtle limit of the effective supergravity description can be defined — giving rise to a non-relativistic analog of NS-NS gravity. The results are compared with constraints on the background geometry coming from (one-loop) beta function calculations. In the final part of my talk, I will comment on non-relativistic T-duality, p-brane solutions, and potential applications to non-relativistic holography.

Out-of-time-order correlators (OTOCs) that capture maximally chaotic properties of a black hole are determined by scattering processes near the horizon. This prompts the question to what extent OTOCs display chaotic behaviour in horizonless microstate geometries.

I will first discuss OTOCs for a class of extremal black holes, namely maximally rotating BTZ black holes, and show that on average they display "slow scrambling", characterized by cubic (rather than exponential) growth. Then I will discuss the extent to which these OTOCs are modified in certain "superstrata", horizonless microstate geometries corresponding to these black holes. Rather than an infinite throat ending on a horizon, these geometries have a very deep but finite throat ending in a cap. We find that the superstrata display the same slow scrambling as maximally rotating BTZ black holes, except that for large enough time intervals the growth of the OTOC is cut off by effects related to the cap region.

We study the decay of out-of-time-ordered correlators (OTOC) in an AdS traversable wormhole and its gravity dual, two coupled Sachdev-Ye-Kitaev models ("left" and "right" subsystem). The gravity calculation of OTOC involves perturbative equations more involved than for a black hole, as the perturbation has complex kinematics and can bounce back and forth through the wormhole many times. The outcome is a phase diagram with three regions. One is black-hole like with uniform exponential growth and the Lyapunov exponent $\lambda=2\pi T$ ("the chaos bound"). The intermediate phase has OTOCs with a spectrum of different exponents for different operator modes, all below the maximal chaos bound. The third phase has exponentially small Lyapunov exponents, behaving as $\exp(-1/T)$, in accordance with a recent field-theory calculation in the literature. The Lyapunov spectrum carries more information than just the maximum exponent: it can be related e.g. to teleportation fidelity from left to right subsystem.

Holographic Volume Complexity naturally incorporates the notion of a Momentum/Complexity correspondence. This correspondence formalizes the idea that gravitational clumping of matter increases the complexity of the quantum state. For purely gravitational states, there is no clear momentum candidate aside from perturbative definitions. A generalization of the Momentum/Complexity correspondence is needed to interpret the gravitational contribution as arising from the Weyl tensor of spacetime.

Review lecture on Information geometry and quantum field theory.

The AdS/CFT correspondence is the most prominent example of a duality relating a quantum theory of fields (without gravity) to a gravity theory. As proposed by Maldacena in 1997, the AdS/CFT conjecture is strongly motivated by the duality of D-branes in the open and the closed string theory pictures in the the near-horizon limit. Since then, the question has arisen if a duality relating quantum field theory to gravity may be established more generally, leading to further insights into the structure of quantum gravity. This development is fuelled in particular through new developments involving concepts from quantum information, following the holographic entanglement entropy proposal of Ryu and Takayanagi in 2006. In this talk, I will review very recent progress in this area, considering insights from information geometry, a branch of mathematics, in particular. Moreover, I will consider bulk reconstruction, modular flows, and computational complexity. Insights from black hole physics and information theory have led to new developments in quantum field theory. As examples, I will present implications of the Fisher metric curvature for phase transitions, complexity proposals for conformal field theories and non-local modular flows.

The mild form of the Weak Gravity Conjecture (WGC) requires that (quantum) corrections to extremal charged black holes increase their charge-to-mass ratio. Currently, it is unknown what the minimal assumptions are needed to proof this conjecture. To address this issue, I will reformulate the WGC as a necessary and sufficient condition on the stress tensor. Applied to rotating BTZ black holes, this condition suggests a spinning WGC, which I proof for corrections generated by fields holographically dual to relevant deformations. Imposing both the charged and spinning WGC on a five-dimensional black string and compactifications thereof, I derive new positivity bounds on Wilson coefficients. These bounds are stronger than those obtained from the charged WGC alone and further constrain effective theories compatible with quantum gravity. Based on arXiv:2011.05337 with Alex Cole, Gregory Loges and Gary Shiu.

We identify a set of higher-derivative extensions of Einstein-Maxwell theory that allow for spherically symmetric charged solutions characterized by a single metric function $f(r)=-g_{tt}=1/g_{rr}$. These theories are a non-minimally coupled version of the recently constructed Generalized Quasitopological gravities and they satisfy a number of properties that we establish. We study magnetically-charged black hole solutions in these new theories and we find that for some of them the equations of motion can be fully integrated, enabling us to obtain analytic solutions. In those cases we show that, quite generally, the singularity at the core of the black hole is removed by the higher-derivative corrections and that the solution describes a globally regular geometry. In other cases, the equations are reduced to a second order equation for $f(r)$. Nevertheless, for all the theories it is possible to study the thermodynamic properties of charged black holes analytically. We show that the first law of thermodynamics holds exactly and that the Euclidean and Noether-charge methods provide equivalent results. We then study extremal black holes, focusing on the corrections to the extremal charge-to-mass ratio at a non-perturbative level. We observe that in some theories there are no extremal black holes below certain mass. We also show the existence of theories for which extremal black holes do not represent the minimal mass state for a given charge. The implications of these findings for the evaporation process of black holes are discussed.

The very well-known prescription of Ryu and Takayanagi for computing holographic entanglement entropy (HEE) in Einstein gravity was extended to higher-curvature theories in works by Xi Dong and Joan Camps. Unfortunately, obtaining the entanglement entropy functional involved an obscure procedure in which the Riemann tensors had to be split and weighted according to a certain prescription. In this talk, I will show that there is a much simpler way to understand this procedure, at least when corrections to Einstein gravity are perturbative. By means of this new way to obtain the HEE functional, I will also show some explicit results for cubic theories, employing them to obtain universal terms of the entanglement entropy for various symmetric regions in the boundary field theory. In particular, the universal function characteristic of corner regions in $d=3$ can be shown to be modified by cubic corrections. This is the first example of a holographically obtained corner function different to the Einstein gravity one.

We approach the problem of constructing the holographic dictionary for $AdS_2/CFT_1$ in the context of higher derivative gravitational actions in $AdS_2$. We focus on $S_2$ reductions of four-dimensional $N=2$ Wilsonian effective actions with Weyl squared interactions restricted to constant scalar backgrounds. BPS black hole near-horizon spacetimes fall into this class of backgrounds and, by identifying the boundary operators dual to the bulk fields, we explicitly show how the Wald entropy of the BPS black hole is holographically encoded in the anomalous transformation of the operator dual to a composite bulk field. Additionally, using a 2d/3d lift, we show that the $CFT$ holographically dual to $AdS_2$ is naturally embedded in the chiral half of the $CFT_2$ dual to the $AdS_3$ spacetime, and we identify the specific $CFT_1$ operator that encodes the chiral central charge of the $CFT_2$.

Review lecture on JT gravity.

In this review talk, I will give an overview of several of the main developments in lower dimensional gravity (and in particular Jackiw-Teitelboim (JT) gravity) that have happened in the last couple of years. In particular, emphasis will be placed on the structure and solution of the model in terms of the Schwarzian wiggly curve and Riemann surface technology. At the semi-classical level, this model provides a concrete set-up for understanding some of the recent developments in the information paradox. At the quantum gravity level, higher topological corrections to amplitudes lead to features of discreteness of the underlying system and make contact with Maldacena's version of the information paradox. In particular, JT gravity itself can be written entirely as a matrix integral. We end with some discussions on how generic these lessons are, in particular for other models of quantum gravity.

We use together relativistic hydrodynamics, numerical relativity and holography to address novel problems. We go beyond the state of the art in several directions. First, we construct a gravitational solution of a fully localized, compact black hole falling through the Poincare horizon in an asymptotically $AdS$ setting. By holography, this solution is mapped to a localized plasma surrounded by vacuum that disperses away. Second, we study the applicability of hydrodynamics, and in particular we perform time evolution using causal theories of hydrodynamics, for the first time in the context of holography. Third, we also go beyond the state of the art by performing time evolution of the recent generalized frame formulation of hydrodynamics (BDNK), for the first time. Fourth, our setting constitutes a new arena to the fluid/gravity duality, being outside the usual assumptions. Our results may provide relevant insights into the quark-gluon plasma physics and astrophysical scenarios.

Phase separated states are a key feature of theories with a first order thermal phase transition at infinite volume. Such states can dynamically appear as end states in the real time evolution of the spinodal-instability. Holography stands as an appealing tool in order to simulate out-of-equilibrium, non-linear processes which yield the final phase separated state. In this talk, we will focus on one such process - the dynamics of bubble mergers. We will study the details of the mergers for a range of speeds, including relativistic ones, and we will discuss three different important scenarios.