Abstracts

The perturbative expansions of many physical quantities are divergent, and defined only as asymptotic series. It is well known that this divergence reflects the existence of nonperturbative contributions, such as instanton effects, which are not captured by a perturbative analysis. This connection between perturbative and nonperturbative sectors of a given physical observable can be systematically studied using the theory of resurgence, allowing us to construct a full non-perturbative solution from perturbative asymptotic data. In this lecture I will start by reviewing the essential role of resurgence theory in the description of the analytic solution behind an asymptotic series, and its relation to the so-called Stokes phenomena, phase transitions and ambiguity cancelations. I will then present the most recent applications of resurgence in the context of string and gauge theories.

We present a study of $\mathcal{N}=4$ supersymmetric QED in three dimensions, on a three-sphere, with $2N$ massive hypermultiplets and a Fayet-Iliopoulos parameter. We identify the exact partition function of the theory with a conical (Mehler) function. This implies a number of analytical formulas, including a recurrence relation and a second-order differential equation. In the large $N$ limit, the theory undergoes a second-order phase transition on a critical line in the parameter space. We will discuss the critical behavior and compute the two-point correlation function of a gauge invariant mass operator.

(Joint work with Jorge G. Russo, arXiv:1610.08527)

We recently showed that the Bethe equations for $AdS_3$ integrability describe the spectrum of a much smaller sector than was the case for $AdS_5/CFT_4$. The reason is that wrapping corrections enter much earlier than before, thanks to the presence of massless modes. This explains a mismatch that was seen in one of the classic tests of AdS/CFT integrability, namely the study of circular spinning strings from which Hernandez & Lopez deduced the one-loop dressing phase for AdS5. Several other mismatches may be caused by the same physics.

We consider mixed branches of $3d$, $N=4$, $T[SU(N)]$ theories. Motivated by the type IIB brane construction, we propose a restriction rule acting on the Hilbert Series of the full Coulomb branch that will truncate the magnetic charge summation only to the subset of BPS dressed monopole operators that arise in the Coulomb branch part of a given mixed branch. We check this proposal in explicit examples, and we further generalize it to the Higgs branch part of a given mixed branch, by exploiting $3d$ mirror symmetry. As a result, we are able to compute the Hilbert Series of any mixed branch of $T[SU(N)]$.

New relations between wall crossing invariants, such as the BPS monodromy, and various limits of superconformal indices of 4d N=2 theories have been recently proposed. For theories of class S on their Coulomb branches, spectral networks provide a way to compute BPS monodromies directly, in a neighborhood of the superconformal point. Several new results on BPS monodromies can be obtained in this way, bringing new insights into these correspondences.

Holography allows us to formulate questions about quantum gravity in terms of more ordinary quantum field theories without gravity. A natural and long-standing goal has been to understand the physics of black holes using holographic duality. I will report on some recent progress on this question formulating the spherical collapse of an in-falling shell of null matter in three dimensions in terms of a first-principles CFT calculation. I will argue that the apparent loss of information in the CFT can be traced back to late-time non-perturbative effects in an expansion in large central charge.

We explore the question of which shape a manifold is compelled to take when immersed into another one, provided it must be the extremum of some functional. We consider a family of functionals which depend quadratically on the extrinsic curvatures and on projections of the ambient curvatures. These functionals capture a number of physical setups ranging from holography to the study of membranes and elastica. We present a detailed derivation of the equations of motion, known as the shape equations, placing particular emphasis in the issue of gauge freedom in the choice of normal frame. We apply these equations to the specific case of holographic entanglement entropy for higher-curvature three-dimensional gravity and find new classes of entangling curves. In particular, we discuss the case of New Massive Gravity where we show that non-geodesic entangling curves have always a smaller on-shell value of the entropy functional. Nevertheless, the correct value for the entanglement entropy is provided by geodesics. Then, we discuss the importance of these equations in the context of classical elastica and comment on terms that break gauge invariance.

We propose a holographic computation of the $2 \to 2$ meson scattering in a curved string background, dual to a QCD-like theory. We recover the Veneziano amplitude and compute a perturbative correction due to the background curvature. The result implies a small deviation from a linear trajectory, which is a requirement of the UV regime of QCD.

We investigate the effect of external magnetic fields on equilibration in the improved holographic QCD theory in the deconfined phase using the AdS/CFT correspondence. In particular we calculate the quasinormal mode spectra in the corresponding black brane solutions and study their dependence on temperature, momentum and magnetic field, both in the scalar and the shear channels. We find complex patterns in the motion of quasinormal modes on the complex plane, including certain cross overs between the lowest lying modes under varying magnetic field, momentum and temperature. We also discover a critical value of the magnetic field Bc above which the hydrodynamic approximation breaks down, as the imaginary part of the first excited quasi-normal mode in the shear channel becomes smaller than that of the hydro mode.

Axion models can be described in terms of a 3-form eating a 2-form dual to the axion. I will discuss how stringy axions can give rise to potentials for the axion in this language, where there is naively no candidate 3-form to eat up. The necessary 3-form will arise when taking into account the backreaction of the instanton in the underlying geometry. Novel applications of this mechanism and ongoing research might also be presented. Based on arXiv:1605.08092 and ongoing work.

I review recent boundary conditions in AdS suitable for observers near a black hole horizon. I focus on 3-dimensional Einstein gravity and discuss consequences of these new boundary conditions, in particular the emergence of soft Heisenberg hair and its role for BTZ black hole microstates. Generalizations to flat space, higher derivatives, higher spins and higher dimension are addressed.

We review black holes in the $1/D$ expansion.

We calculate the Kaluza-Klein spectrum of spin-2 fluctuations around the ${\cal N}=3$ warped $AdS4 \times M6$ solution in massive IIA supergravity. This solution was conjectured to be dual to the $D=3 {\cal N}=3$ superconformal $SU(N)$ Chern-Simons matter theory with level k and 2 adjoint chiral multiplets. The $SO(3)_R×SO(3)_D$ isometry of the ${\cal N}=3$ solution is identified with the $SU(2)_F×SU(2)_R$ global symmetry of the dual ${\cal N}=3$ SCFT. We show that the $SO(3)_R×SO(3)_D$ quantum numbers and the AdS energies carried by the BPS spin-2 modes match precisely with those of the spin-2 gauge invariant operators in the short multiplets of operators in the ${\cal N}=3$ SCFT. We also compute the Euclidean action of the ${\cal N}=3$ solution and the free energy of the ${\cal N}=3$ SCFT on $S^3$, in the limit $N \gg k$. Remarkably, the results show a complete agreement.

Exceptional generalised geometry provides a language with which one can naturally describe M theory and type II with fluxes. In this talk I will show how G-structures defined on the generalised tangent bundle of the internal compactification space which are torsion-free with respect to the exceptional Dorfman bracket are in one-to-one correspondence with Minkowski backgrounds preserving supersymmetry -- they are the precise analogue of the Calabi-Yau conditions for arbitrary flux compactifications, and their solutions are likewise Ricci-flat in the generalised geometric sense. N=1 AdS flux backgrounds can also be neatly described in this formalism, the torsion-free condition being minimally relaxed to accommodate the cosmological constant, yielding generalised Einstein spaces for the geometry of the internal space.

In this talk I will present an extended field theory that captures the full $SL(2) \times O(6,6+n) $ duality group of $N=4$ supergravity in four dimensions. Making use of the $SL(2) $ structure, I will show how to generate gaugings at $SL(2)$ angles via generalised Scherk-Schwarz ansätze. Such gaugings allow for moduli stabilisation including the $SL(2)$ dilaton.

One of the great success of string theory is the microscopical explanation of the entropy of a class of asymptotically flat black holes. Much less is known about asymptotically AdS black holes in four dimensions or higher. In this talk I explain how to derive the entropy of a class of asymptotically AdS supersymmetric black holes in four dimensions using holography. The counting of black hole micro-states is related to a counting of states in the dual three-dimensional gauge theory which can be explicitly performed using localization.

We will discuss recent progress in the CFT interpretation of non-Abelian T-duality in AdS string theory backgrounds. We will focus on $AdS_5$ and $AdS_4$ examples for which the dual CFT can be identified as specific linear quivers. This reveals an interesting set-up in which non-Abelian T-duals of $AdS_{p+1}$ backgrounds are related to Dp-D(p+2)-NS5 brane intersections.

I will describe the smooth microstate geometries with non-Abelian fields found in 1608.01330. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of $N=1$ $ d=5$ Super-Einstein-Yang-Mills theory of supergravity, having the asymptotic charges of a black hole or black ring but with no horizon. The result provides the first approach to understand the microstate structure of non-Abelian black holes.

It is known from the work of Horowitz and Welch that in supergravity black hole entropy is invariant under the action of $T$-duality. What happens when $\alpha'$ corrections are included? I will present an $\alpha'$ corrected family of actions -including Type II, bosonic and heterotic strings- that enjoy $T$-duality symmetry. After that, I will show the form of the entropy and its behaviour under the corrected T-duality.

The overall theme of this talk is whether one can find a unifying framework that can connect the gauge and string theory sides of the AdS/CFT correspondence, thus enabling one to quantitatively connect the two sides. This would enable one to study quantitatively how space, time and gravity emerge from a quantum theory. In the planar regime, the integrable spin chain provides such a unifying framework but it cannot be used beyond planar gauge theory and tree-level string theory. Our proposal is that Spin Matrix theory provides a unifying framework near certain unitarity bounds, enabling one to access finite-$N$ effects. We give evidence for this by matching non-supersymmetric dynamics of D-branes on $AdS_5 \times S^5$ to a finite-$N$ regime in $N=4$ SYM near a unitarity bound. In particular, we find an effective matrix model that describes the dynamics of weakly interacting giant gravitons wrapped on three-spheres in the AdS part of $AdS_5 \times S^5$ at high energies using the non-abelian DBI action. In parallel we consider the limit of $N=4$ SYM near a certain unitarity bound where it reduces to the quantum mechanical theory called $SU(2)$ Spin Matrix theory. We show that the exact same matrix model that describes the giant gravitons on the string theory side also provides the effective description in the strong coupling and large energy limit of the Spin Matrix theory.

I will give an overview of the relations expressing gravity as a "double copy" of gauge theory. These relations appeared first in string theory, and have been used to compute scattering amplitudes in theories of (super)gravity. At the level of perturbative amplitudes, I will review current research topics such as the colour-kinematics duality in gauge theory and the new formalism of the scattering equations. I will then discuss the extension of the double-copy procedure to classical solutions in general relativity, including our best known black hole spacetimes.

Originally formulated in the 70's, the conformal bootstrap is the ambitious idea that one can use internal consistency conditions to carve out, and eventually solve, the space of conformal field theories. In this talk I will review recent developments in the field which have boosted this program to a new level.

I will present a method to extract quantitative informations in strongly-interacting theories, such as 3D Ising, $O(N)$ vector model and even systems without a Lagrangian formulation. I will explain how these techniques have led to the world record determination of several critical exponents.

We show how one can construct the N=2 matter coupled supergravity theory as a product of N=2 SYM with a bosonic theory. We use the gauge-gravity dictionary obtained to build multi-centered BPS black hole solutions from SYM BPS solutions.

We discuss the bootstrap program applied to four-dimensional $N=2$ superconformal field theories, with special focus on analytical results. As a particular case we also consider the recently found $N=3$ SCFTs in four dimensions. We constrain the allowed space of SCFTs by making use of the existence of a protected subsector captured by a two-dimensional chiral algebra. Finally we discuss implications for the numerical bootstrap program.

We exploit the examples of constrained superfields that appear in some supergravity cosmological models to put forward an interpretation of superfields that makes use of basic algebraic geometry tools as schemes or its super version, superschemes, perhaps not well known in the physics literature. In this way, non regular superschemes are shown to appear naturaly from physical constraints which challenge the standard interpretations.

One mysterious facet of M-theory is how a 10-dimensional string theory can "grow an extra dimension" to become 11-dimensional M-theory. Physically, the process is understood via brane condensation. Mathematically, Fiorenza, Sati, and Schreiber have proposed that brane condensation coincides with extending superspacetime, viewed as a Lie superalgebra, by the cocycle in Lie algebra cohomology which encodes the brane's WZW term. The resulting extension can be regarded as an "extended superspacetime'' where still other super p-branes may live, whose condensates yield further extensions, and so on. In this way, all the super p-branes of string theory and M-theory fit into a hierarchy called "the brane bouquet". In this talk, we show how the brane bouquet grows out of the simplest kind of supermanifold, the superpoint.

This is joint work with Urs Schreiber.

AdS/CFT has given us an unprecedented new holographic window in strongly coupled physics. In particular the existence of charged black holes in AdS predicts the existence of novel quantum critical fixed points distinct from the conventional theory of critical phenomena. The distinct features of these novel quantum critical points show a remarkable resemblance with the profoundly mysterious behavior of exotic strange metal states of quantum matter, e.g. in high Tc superconductors. Recent experiments strongly indicate that this resemblance is more than superficial. This has put us at the cusp of a new era in theoretical physics: we will present the case that current experiments can and will test a holographic gravity model as the theory of the strange metal state.

Weyl semimetals (WSMs) are novel gapless topological states of matter with electronic low-energy excitations behaving as left- and right-handed Weyl fermions. Remarkably this is the first known experimental realization of Weyl fermions. As in topological insulators, the existence of surface states is guaranteed by topology. Moreover, it has been shown that the surface states of a WSM form so-called Fermi arcs connecting the projections of the Weyl nodes onto the surface Brillouin zone. I will discuss these states at strong coupling within the so called Holographic Weyl Semimetal.

It has been conjectured that the speed of sound in holographic models with UV fixed points has an upper bound set by the value of the quantity in conformal field theory. If true, this would set stringent constraints for the presence of strongly coupled quark matter in the cores of physical neutron stars, as the existence of two-solar-mass stars appears to demand a very stiff Equation of State. In this article, we present a family of counter examples to the speed of sound conjecture, consisting of strongly coupled theories at finite density. The theories we consider include N = 4 super Yang-Mills at finite R-charge density and non-zero gaugino masses, while the holographic duals are Einstein-Maxwell theories with a minimally coupled scalar in a charged black hole geometry. We show that even for a small breaking of conformal invariance, the speed of sound approaches the conformal value from above at large chemical potentials.

Holography for UV-incomplete gauge theories is important but poorly understood. A paradigmatic example is d=4, N=4 super Yang-Mills coupled to $N_f$ quark flavors, which possesses a Landau pole at a UV scale $ΛLP$. The dual gravity solution exhibits a UV singularity at a finite proper distance along the holographic direction. Despite this, holographic renormalization can be fully implemented via analytic continuation to an AdS solution. The presence of a UV cut-off manifests itself in several interesting ways. At energies $E \ll ΛLP$ no pathologies appear, as expected from effective field theory. In contrast, at scales $E \lesssim ΛLP$ the gravitational potential becomes repulsive, and at temperatures $T \lesssim ΛLP$ the specific heat becomes negative.

I will show how the tensor hierarchy of generic, bosonic, $8$-dimensional field theories is built. Studying the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations we determined the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the $6$-forms and also the equations of motion. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them. With the results at hand I will show how to construct explicitly a $1$-parameter family of $SO(3)$-gauged maximal $d=8$ supergravities that interpolates continuously between the theory constructed by Salam and Sezgin by Scherk-Schwarz compactification of $d=11$ supergravity and the theory constructed in arXiv:hep-th/0012032 by dimensional reduction of the so called massive $11$-dimensional supergravity proposed by Meessen and Ortín earlier.

The talk is based on the articles: arXiv:hep-th/1605.05882v1, arXiv:hep-th/1605.09629v2.

Recently, a flux of ideas from the theory of quantum chaos and quantum complexity has influenced discussions of black hole dynamics in the framework of holography. In this talk I will attempt a review of these developments.

Twenty years after the Maldacena model for holography, new entries for the AdS/CFT dictionary are still being created. After a brief review of holographic entanglement entropy and its interpretation in terms of tensor networks, I will introduce some recent proposals about the bulk dual to the quantum computational complexity. With these tools, we compute the complexity of a peculiar degenerate system, i.e. near-extremal hyperbolic black holes, and study its anomalous behavior.

We introduce classical holographic codes. These can be understood as concatenated probabilistic codes and can be represented as networks uniformly covering hyperbolic space. In particular, classical holographic codes can be interpreted as maps from bulk degrees of freedom to boundary degrees of freedom. Interestingly, they are shown to exhibit features similar to those expected from the AdS/CFT correspondence. Among these are a version of the Ryu-Takayanagi formula and intriguing properties regarding bulk reconstruction and boundary representations of bulk operations. We discuss the relation of our findings with expectations from AdS/CFT and, in particular, with recent results from quantum error correction.

Conformal mass in AdS gravity encodes the physical information about conserved charges of a system in the electric part of the Weyl tensor. Based on the Noether theorem, we show that the conformal mass can be defined for any Lovelock AdS gravity, provided the AdS vacuum is a non-degenerate solution of the field equations. We find an explicit expression for the conformal mass in this case.

We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. We show that causality and unitarity are compatible with each other and they both require the Newton constant to be negative. This is in contrast with what happens in the higher dimensional case. We discuss the reasons behind this result.