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.

I will argue that a semiholographic framework can lead us to unravel general aspects of many quantum many body systems with strongly interacting degrees of freedom. I will present the case for QCD and some other QFTs. In particular, applications to heavy ion physics and hadronic physics will be discussed. A derivation of the framework combining exact Wilsonian RG and holographic RG will be sketched.

We discuss implications of unitarity in CFTs and derive a number of constraints, including positivity of energy flux constraint.

I will review some recent progress about superconformal field theories in six dimensions. A simple class has an effective description in terms of a chain of gauge fields, coupled by tensors and hypermultiplets. Their holographic duals are now known analytically, and some precision checks can be performed, involving Weyl anomalies. An extension of this class can be studied using F-theory. All these theories have some features in common with the elusive theory describing M5-branes, and indeed suggest new phenomena, such as M5 fractionation.

I will discuss what we have learned in the past year about transport in strongly interacting metallic phases by studying the linear response of planar black holes with broken translational symmetry. Firstly, I will discuss how holography tells us that the conductivity of weakly disordered metals is described by the Drude formula, confirming a "prediction" of the many-body memory matrix approach. Secondly, I will discuss the derivation of non-perturbative conductivity bounds, invoking a new version of the holographic membrane paradigm. These bounds rule out disorder-driven phase transitions (which would generically exist in traditional condensed matter models) in the boundary theory under rather mild assumptions about the existence and nature of solutions to Einstein's equations. Connections between these black-hole inspired theories of transport and novel experiments in graphene will also be discussed.

In this talk I will discuss superconformal theories in four dimensions obtained wrapping M5 branes on a Riemann surface. I will first review N=2 class S theories introduced some years ago by Gaiotto and then describe a generalization to the N=1 case. For this class of theories it is possible to write down a spectral curve encoding the properties of the chiral ring and I propose a method to determine from the spectral curve the scaling dimension of chiral operators in the SCFT. This proposal reduces to the correct prescription in the special case of N=2 theories. I will provide several consistency checks and apply this method to study some new superconformal theories.

We derive the one-instanton effective action of N=4 super Yang-Mills theory in terms of the N=4 on-shell superfields. In the Coulomb branch, instantons correct both the MHV and next-to-next-MHV higher derivative terms D^4F^{2n+2} and F^{2n+4}. We confirm at the non-perturbative level the non-renormalization theorems for MHV F^{2n+2} terms that are expected to receive perturbative corrections only at n-loops. We compute also the one and two-loop corrections to the D^4F^4 term and show that its completion under SL(2,Z) duality is consistent with the one-instanton results.

Non-equilibrium black hole horizons are considered in scaling theories with generic Lifshitz invariance and an unbroken U(1) symmetry. There is also charge-hyperscaling violation associated with a non-trivial conduction exponent. The boundary stress tensor is computed and renormalized and the associated hydrodynamic equations derived. Upon a non-trivial redefinition of boundary sources associated with the U(1) gauge field, the equations are mapped to the standard non-relativistic hydrodynamics equations coupled to a mass current and an external Newton potential in accordance with the general theory of [arXiv:1502.00228]. The shear viscosity to entropy ratio is the same as in the relativistic case.

Holography is a tool that can be most readily applied to studies of transport properties in gauge theories with infinitely strong interactions. Coupling constant corrections can then be incorporated through higher-derivative (alpha-prime) corrections to the supergravity action in the bulk. In the first part of this talk, I will discuss the dependence of higher-order hydrodynamic transport (beyond Navier-Stokes) and the higher-frequency (quasi-normal) spectrum on the coupling constant in duals of Type IIB supergravity and curvature-squared theories. In relation to the membrane paradigm, I will then present higher-order generalisations of the universal "eta over s" relation and universal anomalous conductivities at finite coupling. Recently, studies of holographic transport in the presence of broken translational symmetry and disorder have received much attention. In particular, it has been shown how thermo-electric conductivities can be computed by using the membrane paradigm. Through the power of the membrane paradigm and with a view towards future models of many-body localisation without hydrodynamic transport, in the second part of this talk, I will discuss the proofs of the lower bounds on thermal and electrical conductivities in a large family of holographic theories with arbitrarily strong disorder.

After a review of the quasinormal mode method for partition function calculation developed by Denef, Hartnoll, and Sachdev, we study a scalar in AdS2. We find a series of zero modes with negative real values of the conformal dimension whose presence indicates a series of poles in the one-loop partition function. The contribution of these poles to the AdS partition function at physical mass values matches previous results. Additionally, extending our results to AdS in any even dimension 2n, we find a similar series of zero modes related to discrete series representations of SO(2n,1), and successfully calculate the one-loop determinant from these modes. Finally, we speculate on the physical meaning of these non-physical-mass modes.

We compute the heat kernel for the Laplacians of symmetric transverse traceless fields of arbitrary spin on the AdS background in even number of dimensions using the group theoretic approach and apply it on the partition function of six dimensional conformal gravity. The obtained partition function consists of the Einstein gravity, conformal ghost, partially massless mode and massive mode.

Matrix models are toy models for quantum field theories. They can be extremely complicated but can also be solved in a variety of ways. In my talk I will discuss general properties of matrix models and their solutions and focus on particular matrix models that arise in the study of 4d SUSY field theories. Those matrix models describe the index of the field theory, counting the number of states of the theory (with + sign for a boson and - for a fermion) and have been known for over 10 years. Though they look very complicated I will show how some simple tricks allow in certain cases to solve those matrix models exactly in terms of elementary functions. My talk will focus on the matrix model calculation and no specialized knowledge of SUSY field theories or indices would be required to follow it.