abstract

In this article, we give a pedagogical introduction into integrable models. First, we review how classical integrable models can be constructed by demanding the existence of a higher spin conserved charge. The primary examples are the sinh-Gordon and sine-Gordon theories whose classical integrability is exactly shown by exploiting the Bäcklund transformation. Lagrangian quantization together with the LSZ reduction formula provide insight into the functional properties and analytical structure of the scattering matrices. These are the inputs in the S-matrix bootstrap program, which determine the scattering matrices from global symmetries, crossing and unitarity properties. Then it is shown how the scattering matrices can be used to calculate the large volume spectrum of the theory. We end the paper by overviewing the literature where the various steps of the analogue integrable developments in the AdS/CFT correspondence were developed.

abstract

Three-dimensional gravity is known as a powerful arena to explore non-perturbative aspects of quantum gravity. A particularly useful corner has been the Chern–Simons formulation of higher spin gravity in AdS\(_3\): this setup allows us to explore and test the lore behind black-hole mechanics in a theory that lacks a metric description. In this lectures, we will review recent developments in this subject; in particular, we will emphasize on various definitions of black holes in AdS\(_3\) and how to probe them using the observables that naturally arise in the Chern–Simons theory.

abstract

We review construction of the improved holographic models for QCD-like confining gauge theories and their applications to the physics of the quark–gluon plasma. We also review recent progress in this area of research. The lecture notes start from the vacuum structure of these theories, then develop calculation of thermodynamic and hydrodynamic observables, energy loss and momentum broadening of heavy probes, and end with more advanced topics such as the holographic QCD in the presence of external magnetic fields. This is a summary of the lectures presented at the LVI Cracow School of Theoretical Physics in spring 2016 at Zakopane, Poland.

abstract

In the course of the past several years holography has emerged as an ab initio tool in exploring strongly time-dependent phenomena in gauge theories. These lecture notes overview recent developments in this area driven by phenomenological questions concerning applicability of hydrodynamics (hydrodynamization) under extreme conditions occurring in ultrarelativistic heavy-ion collisions at RHIC and LHC. The topics include hydrodynamization time scale, holographic collisions, as well as hydrodynamization from the point of view of the asymptotic character of the hydrodynamic gradient expansion. The emphasis is put on concepts rather than calculational techniques, and a particular attention is devoted to present these developments in the context of the most recent advances and some of the open problems.

abstract

Chiral anomalies give rise to dissipationless transport phenomena such as the chiral magnetic and vortical effects. In these notes, I review the theory from a quantum field theoretic, hydrodynamic and holographic perspective. A physical interpretation of the otherwise somewhat obscure concepts of consistent and covariant anomalies will be given. Vanishing of the CME in strict equilibrium will be connected to the boundary conditions in momentum space imposed by the regularization. The role of the gravitational anomaly will be explained. That it contributes to transport in an unexpectedly low order in the derivative expansion can be the most easily understood via holography. Anomalous transport is supposed to play also a key role in understanding the electronics of advanced materials, the Dirac and Weyl (semi-)metals. Anomaly related phenomena such as negative magnetoresistivity, anomalous Hall effect, thermal anomalous Hall effect and Fermi arcs can be understood via anomalous transport. Finally, I briefly review a holographic model of Weyl semi-metal which allows to infer a new phenomenon related to the gravitational anomaly: the presence of odd viscosity.