We will discuss two classes of line defects in the O(N) critical model at the Wilson-Fisher fixed point. These extended excitations are relevant for condensed matter systems, such as doped quantum antiferromagnets. After reviewing some state-of-the-art analytic bootstrap techniques, we will apply them to compute the correlator of two bulk excitations at first order in the epsilon expansion. From this result we are able to extract an infinite set of defect CFT data.

I will give a summary of recent progress in the computation of exact results in the presence of superconformal defects, focusing on a special class of defect correlators. Along the way, I will comment on the possibility of using integrability and propose various future directions. NOTE: to receive the link please fill the registration form at integrability-london.weebly.com

In the last fifteen years an extensive and successful program has been carried out, consisting in the application of integrability techniques to the study of the AdS/CFT correspondence in the planar limit. In this talk we focus on a particular string background corresponding, on the dual side, to the expectation value of a cusped Wilson line. Recently the study of this background has been boosted by the OPE program for polygonal Wilson loops and scattering amplitudes. In this talk we consider the quantum fluctuations of the worldsheet theory around the null cusp classical solution and we investigate various quantities of physical interest (free energy, dispersion relation, S-matrix) in the perturbative expansion at strong coupling. We also propose a possible discretization of this model which can be used to study the theory non-perturbatively through numerical lattice simulations.