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.

Entanglement entropy is a very important quantity in holography, nevertheless it is only a measure of the total amount of entanglement between two complementary subsystems in a global pure state. A more detailed knowledge about the pattern of entanglement is essential for a deeper understanding of the relation between bulk geometry and quantum information in the boundary theory. I will discuss how negativities and other measures can be used in this context focusing in particular on qubit systems for which a classification of possible entanglement structures is available.

In this talk, I will summarize recent progress in the description of thermoelectric transport using gauge/gravity duality. I will first review thermoelectric transport in hydrodynamics, where momentum conservation implies infinite zero-frequency conductivities. By a change of basis of the conserved currents, a universal, finite conductivity can be extracted. It can be computed holographically. I will discuss its low-temperature scaling in terms of critical exponents characterizing time and space anisotropy and anomalous dimensions for the free energy and conserved current. When momentum is almost conserved, the zero-frequency delta functions broaden into Drude-like peaks. A holographic computation precisely identifies the redistribution of the low-frequency spectral weight between two contributions originating from the non-conservation of momentum and intrinsic dissipation respectively. It also sheds some light on how to construct effective theories of thermoelectric transport when momentum is not conserved.

Gauge/gravity duality can be used to study the transport properties of strongly interacting systems with no quasi-particles. I will give an overview of some holographic toy models of states like this, in which momentum is not conserved and thus the transport of energy and charge is non-trivial. Specifically I will discuss the thermoelectric transport properties of these toy models and their possible relations to the phenomenology of the strange metals.

Describing work in collaboration with Louise Dolan, I will discuss the scattering equations, originally introduced in 1972 by Fairlie and Roberts searching for new dual models, rediscovered by Gross and Mende in 1988, discussing the high energy behaviour of string theory, and more recently shown by Cachazo, He and Yuan to provide a kinematic basis for describing remarkable formulae for tree amplitudes for massless particles in arbitrary space-time dimension (including scalars, gauge bosons and gravitons). We reformulate the scattering equations for N particles as a system of N -3 homogeneous polynomial equations in N - 2 complex variables, which are linear in each variable separately. The linearity of the equations enables their explicit solution in terms of the roots of a single-variable polynomial of degree (N-3)!, which can itself be explicitly constructed in terms of the Mandelstam variables formed from the momenta. The possible extension to one loop and the special case of four-dimensional space-time will also be briefly discussed.

The recent focus on entanglement entropy in holography has many motivations, ranging from the applied (e.g. AdS/CMT) to the foundational (emergence of gravity). For all of these programs It is important to find examples, where the quantities of interest can be directly calculated in strongly-coupled field theories and, moreover, the dual geometry constructed at strong coupling. In this talk I will describe joint work with Crossley and Dyer on using localization methods to obtain entanglement and (super-) Renyi entropies of the N=4 SYM theory with gauge group SU(N) in 4D at all values of the ’t Hooft coupling \lambda and number of colors N. Since obtaining quantities like entanglement and Renyi entropies involves working on singular spaces, which typically break the supersymmetry, we focus on a supersymmetric generalization, the so-called super-Renyi entropy where the supersymmetry breaking effects of the singularities are suitably compensated. I will also discuss dual gravity solutions as five-dimensional BPS black holes with hyperbolic horizon. I will conclude with a description of Wilson loops, that is the contribution to the entanglement and Renyi entropies due to adding fundamental matter to the theory.

While a lot of work has been done on understanding thermalization in 2d CFTs, several confusing aspects remain, in particular regarding integrable aspects of 2d CFTs. In this talk I will try to summarize some of these confusions and how these connect to AdS/CFT and black hole formation. There appears to be a significant difference between thermalization in low c CFTs versus thermalization in large c CFTs with gravitational duals.

Certain materials, such as the cuprate superconductors and heavy fermion materials exhibit fascinating, yet hard to explain transport properties. Holography provides a consistent framework to examine linear response and in particular transport of strongly coupled matter. I will discuss momentum dissipation in holography and show that DC transport is fixed via a Stokes flow of an "auxiliary fluid" residing on the horizon of black holes.

I will discuss knot-like defects in CS theory with complex gauge group SL(N), in the context of its connection with 3d N=2 theory (the so-called 3d-3d correspondence). I am hoping to discuss this problem from a number of different perspectives, including cluster algebras, state-integral models, 3d N=2 non-Abelian gauge theories, 5d N=2 SYM, and holographic dual, and discuss the consistency checks as well as new predictions/implications. This talk is mostly based on my recent papers with D. Gang, N. Kim and M. Romo.

Dual superconformal symmetry is a remarkable, hidden feature of N=4 SYM in 4 dimensions. Via AdS/CFT, such a symmetry corresponds to the invariance of the AdS(5) x S(5) superstring under specific combinations of bosonic and fermionic T-dualities. We show that AdS(d) x S(d) x S(d) superstrings with D(2,1;\alpha) isometry supergroup are T-self-dual if additional T-dualities along complexified S(d) directions are performed. This implies that CFTs dual to AdS(d) x S(d) x S(d) x T(10-3d) superstrings enjoy a new type of dual superconformal symmetry.