The so-called 6d (2,0) conformal field theory in six dimensions, labeled by an ADE Lie algebra, has become of great interest in recent years. Most notably, it gave new insights into lower dimensional supersymmetric field theories, for instance in four dimensions, after compactification. In this talk, I will talk about a deformation of this CFT, the six-dimensional (2,0) little string theory: its origin lies in type IIB string theory, compactified on an ADE singularity. We further compactify the 6d little string on a Riemann surface with punctures. The resulting defects are D-branes that wrap the 2-cycles of the singularity. This construction has many applications, and I will focus on one: I will provide the little string origin of the classification of surface defects of the 6d (2,0) CFT, for ADE Lie algebras. Furthermore, I will give the physical realization of the so-called Bala-Carter labels that classify nilpotent orbits of these Lie algebras.

We numerically construct asymptotically global AdS_5xS^5 black holes that are localised on the S^5. These are solutions to type IIB supergravity with S^8horizon topology that dominate the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS_5-Schwarzschild x S^5. By the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N=4 supersymmetric Yang-Mills down to SO(5). We extrapolate the location of this phase transition and compute the expectation value of a scalar operator in the low energy phase. In addition, we discuss the construction of localised black holes in type IIA, which are dual (via T-duality) to the low temperature phase of thermal 1+1 dimensional supersymmetric Yang-Mills theory on a circle.

The N-extended massless superparticle in a 4D Minkowski background has a worldline time-reversal invariance that becomes CPT in the quantum theory. This symmetry is anomalous for odd N, which explains why there is no CPT-self-conjugate massless supermultiplet for N=1. In the supertwistor formulation of superparticle mechanics, the anomaly is a close cousin of the parity anomaly of 3D gauge theories. CPT is not anomalous if N is even but if 2N is odd there is a Kramers degeneracy, which explains why the N=2 hypermultiplet is a doubled version of the CPT-self-conjugate supermultiplet of helicities (-1/2,0,0,1/2).

I'll give an introduction to N=2, D=4 SCFTs of "Class-S" and a survey of our programme for classifying such theories. I will put special emphasis on the theories arising from the Exceptional (2,0) SCFTs in D=6.

I will discuss recent advances in addressing the heterotic moduli problem in six and seven dimensions. To map out the reduction to a lower dimensional effective theory, and in a quest to complete our understanding of the generically torsional geometries that appear, it is important to understand the moduli of these geometries. I will briefly review the infinitesimal moduli space in six dimensions, and comment on some recent advances in understanding its geometric properties. I will then explain how a similar story is emerging in seven dimensional compactifications on more exotic manifolds with G2-structure, giving hope that similar tools can be applied to understand moduli in other areas of string theory, with possible applications to phenomenology and AdS/CFT. If time, I will comment on some recent advances is studying finite deformations and obstructions of the moduli space.

Abstract: We are using holography to study quantum phase transitions in a 2+1 D strongly coupled non conformal gauge theory at finite chemical potential and magnetic field B. Our gravity dual is 4D N = 2 Fayet-Iliopoulos gauged supergravity. We found a line of quantum critical points at B= Bc between extremal dyonic black branes and extremal magnetically charged "thermal gas" solutions. We will introduce the two types of solutions, their thermodynamics and their phase diagram. Then we will discuss the physics of the critical point and we will point out qualitative similarities between our field theory and Nambu- Jona- Lasinio model in 2+1 D under the presence of an external magnetic field. We will conclude with some open questions both on the gravity and field theory side and we will discuss future directions.

In this talk I will describe recent progress towards understanding integrable deformations of superstrings in AdS backgrounds. One well-known example of such a deformation is the TsT transformation, which involves a T-duality, a shift introducing the deformation parameter, and a reverse T-duality. After introducing this deformation, I will give two alternative constructions: (i) as a particular non-abelian duality, and (ii) as a particular Yang-Baxter deformation. In the second part of the talk I will outline how this extends to a general relationship between non-abelian duality and Yang-Baxter deformations, and discuss the consequences for the Weyl invariance of the deformed models.

We consider the four-point correlator of the stress tensor multiplet in N = 4 SYM in the limit of large c=N^2, but finite \lambda=g^2 N. For finite values of \lambda single-trace intermediate operators arise at order 1/c and this leads to specific poles in the Mellin representation of the correlator. The sign of the residue at these poles is fixed by unitarity. We consider solutions consistent with crossing symmetry and this pole structure. We show that in a certain regime all solutions result in a negative contribution to the anomalous dimension of twist four operators. This positivity condition can also be proven by assuming the correct Regge behaviour for the Mellin amplitude. The positivity constraints arising from CFT for the Mellin amplitude take a very similar form to the causality constraint for the forward limit of the S-matrix.

At low temperature and high quark chemical potential, QCD exhibits color superconducting phases, namely phases in which the color gauge symmetry is spontaneously broken. I will describe work in progress aimed at constructing string duals of gauge theories that exhibit these types of phases.

I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies. I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.

In this talk, I will discuss transport phenomena in two classes of theories with holographic dual. In the first part, I will discuss systems where U(1) current is non-conserved due to anomaly and illustrate how one can show that the anomalous conductivities are non-renormalised in a large class of holographic RG flow. The holographic RG flow we considered is generated by arbitrary dilaton potentials and arbitrary higher derivative terms that do not break global symmetries, incorporating coupling constant corrections to the boundary theory in an expansions around infinite coupling. In the second part, I will focus on systems where translational symmetry is broken by slowly varying scalar fields and show that the bound shear viscosity/entropy density is violate. I will also discuss how to understand the violation in the language of forced fluid dynamics.

In this talk I will start by reviewing the hexagon bootstrap program for three-point functions in N=4. Then I will explain how to extend those methods to ABJM theory by considering three-point functions whose vacua preserve SU(1|2)xU(1) symmetry. I will show that this symmetry fully constraints the two-particle hexagon form factor and comment on how to construct the multi-particle hexagon. Finally, I will conclude with a summary of the difficulties in implementing this program for ABJM.

We give an introduction to twistor theory and construct a twistor action for the self-dual part of conformal higher spin theories by treating the integrability condition for the holomorphic structure of a complex deformation of flat twistor space as the equations of motion of those higher spin fields. Analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, we identify a ghost-free subsector which generates the unique three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints.

Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional at space-time. The models are based on a "map" from stringy hadrons of curved holographic confining backgrounds. In the first part of the talk I will review the "derivation" of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored confining holographic models. I will then describe the string configurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the "string end-point mass" and the "baryonic string vertex". I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will summarize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best fits to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.

In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.

Holography inspired stringy hadrons (HISH) is a set of models that describe hadrons: mesons, baryons, glueballs and exotic hadrons as strings in four dimensional flat space-time. The models are based on a “map” from stringy hadrons of curved holographic confining backgrounds. In the first part of the talk I will review the “derivation” of the models. I will start with a brief reminder of the passage from the original AdS/CFT correspondence to the string/gauge duality of certain favored confing holographic models. I will then describe the string configurations in these holographic backgrounds that correspond to Wilson lines, mesons, baryons, glueballs and exotics. Key ingredients of the four dimensional picture of hadrons are the “string end-point mass” and the “baryonic string vertex”. I will determine the classical trajectories of the HISH spectra. I will review the current understanding of the quantization of these hadronic strings. The computation of HISH decay width of hadrons will be described. In the last part of the talk I will sum-marize the comparison of the outcome of the HISH models with the PDG data about mesons and baryons. I will present the values of the tension, masses and intercepts extracted from best fits to hadron spectra and write down certain predictions for higher excited hadrons. I will present attempts to identify glueballs. The decay width of certain hadrons will be compared with the theoretical calculation. I will suggest a window to the landscape of tetra-quarks and other exotic hadrons.

Mirror symmetry of Calabi—Yau spaces is best understood for families presented as complete intersections in toric varieties; these models have a description as the low-energy limit of Abelian gauged linear sigma models (GLSMs). We investigate the combinatorial conditions on GLSM data such that the generic member of the family determines a non-singular low energy theory. A sufficient condition is reflexivity; this has the pleasant feature that the mirror of a reflexive model is reflexive. This condition is certainly not necessary, in particular it is not preserved by extremal transitions. We propose a weaker condition that is preserved, but is also too strong. Along the way we describe how the Berglund—Hubsch mirror construction is related to the Batyrev—Boris combinatorial duality related to Abelian duality. We study the locus in parameter space along which the model becomes singular and the invariance of this under mirror symmetry, finding support for the observation of Hori and Vafa that mirror symmetry is most naturally stated in terms of local Calabi—Yau models.

I first describe the remarkably simple algebraic structure underlying covariant string field theory. No knowledge of string field theory and only very basic concepts of string theory are required for this. I then use this structure to construct the superstring field theory action recursively and discuss its relation to the decomposition of (super) moduli spaces. I will focus mostly on open string theory but will comment on the generalisation to closed string.

We extend the use of holography to investigate the "Scrambling" (a.k.a "Chaos", "Butterfly Effect", "Thermalization") properties of various physical systems at finite temperature. Specifically, we consider: (i) non-conformal backgrounds of black Dp branes, (ii) asymptotically Lifshitz black holes, and (iii) black AdS solutions of Gauss-Bonnet gravity. We use the disruption of the mutual information as a probe of the chaotic feature of such systems. Our analysis shows that these theories share the same type of behavior as conformal theories as they undergo chaos, however, in the case of Gauss-Bonnet gravity, we find a stark difference in the evolution of the mutual information for negative Gauss-Bonnet coupling. This may signal an inconsistency of the latter.

Quantum field theories in (2+1)-dimensions exhibit a beautiful property known as particle-vortex duality. It relates, in a precise way, two different excitations on the plane, the familiar particle-like excitations that arise from quantisation of the field and vortices, solitonic-excitations defined by the winding of a local order parameter. Originally studied in the context of anyonic superconductivity and Neilsen-Olesen vortices, extensions of the duality have recently found application to, for example, topological quantum matter. I will review some of these developments and show how recent progress in understanding non-abelian T-duality can be used to define a non-abelian particle-vortex duality in (2+1)-dimensions.