We construct topological Wess-Zumino term for supercoset sigma-models on various AdS 3 backgrounds. For appropriately chosen set of parameters, the sigma-model remains integrable when the Wess-Zumino term is added to the action. Moreover, the conditions for integrability, kappasymmetry and conformal invariance are equivalent to each other. * Also at ITEP, Moscow, Russia arXiv:1209.4049v3 [hep-th]

We introduce a series of articles reviewing various aspects of integrable models relevant to the AdS/CFT correspondence. Topics covered in these reviews are: classical integrability, Yangian symmetry, factorized scattering, the Bethe ansatz, the thermodynamic Bethe ansatz, and integrable structures in (conformal) quantum field theory. In the present article we highlight how these concepts have found application in AdS/CFT, and provide a brief overview of the material contained in this series. -mails: diegobombardelli@gmail.com, alessandra.cagnazzo@desy.de, rouven.frassek@durham.ac.uk, fedor.levkovich@gmail.com, loebbert@physik.hu-berlin.de, stefano.negro@lpt.ens.fr, sfondria@itp.phys.ethz.ch, i.m.szecsenyi@durham.ac.uk, svantongeren@physik.hu-berlin.de, a.torrielli@surrey.ac.uk arXiv:1606.02945v2 [hep-th] Jul 2016In this article we introduce a series of articles reviewing aspects of integrable models. The articles provide a pedagogical introduction to the topic of integrability, with special emphasis on methods relevant in the AdS/CFT correspondence. After a brief motivation regarding the value of general integrable models in the development of theoretical physics, here we discuss the application of the framework of integrability to the AdS/CFT correspondence.We then provide an overview of the material contained in the various reviews, referring back to AdS/CFT applications, and indicating links between the reviews themselves and to the relevant literature. While written with an AdS/CFT background in mind, the methods covered in the reviews themselves have applications throughout the wider field of integrability. IntegrabilityIntegrable models appear throughout theoretical physics, starting from classical mechanics where models such as the Kepler problem can be solved-in the sense of the Liouville theorem-by integration. In general, integrable models show special behaviour due to many underlying symmetries, symmetries due to which they can often be exactly solved. Only a fraction of the physical systems appearing in nature can be described in these terms. Nevertheless, integrable models offer insight into real-world situations through universality, or when used as a theoretical laboratory to develop new ideas. In statistical mechanics for example, many subtleties of the thermodynamic limit have been understood by working out specific models, notably phase transitions in the Lenz-Ising model and the role of boundary conditions in the ice model. In hydrodynamics, the Korteweg-de Vries equation illustrates how a nonlinear partial differential equation can admit stable, wave-like localized solutions: solitons. In condensed matter physics, both integrable quantum spin chains and one-dimensional gases of almost-free particles play a pivotal role. Finally, in quantum field theories (QFTs) in two space-time dimensions, exactly solvable models helped unravel phenomena like dimensional transmutation, as in the case of the chiral Gross-Neveu model, or concepts like bosonisation, as in the case of the sine-Go...