Extended probes play a distinguished role in a wide range of physical phenomena ranging from Wilson lines, describing the motion of a heavy charged particle, to twist operators, essential tools for the computation of entanglement entropy. This proposal aims to comprehensively study the non-perturbative dynamics of conformal defects, a class of extended excitations preserving conformal symmetry along their profile. This partial simplification, without spoiling their physical relevance, provides powerful techniques to access the finite coupling regime. More specifically, the final goal of the project is to obtain exact results for strongly coupled conformal field theories in the presence of defects. In this context, it is convenient to start from the most symmetric case, when conformal invariance is supplemented by supersymmetry. This proposal will employ a systematic approach to the study of superconformal defects, exploring their non-perturbartive regime using several different techniques, such as supersymmetric localization, integrability and the holographic correspondence. The latter, in particular, establishes a non-trivial connection between conformal field theories and quantum gravity, allowing for a fruitful interplay between very different theories. The second part of this proposal focuses on the more general methods of the conformal bootstrap, which is based on the general philosophy that the symmetries of a conformal field theory are sufficient to completely determine its dynamics. Recent analytic developments in this direction will be applied to defect conformal field theories with and without supersymmetry. The results of the research carried out during the project are expected to considerably improve our understanding of conformal defects. They will be published in high impact journals and effective measures for the dissemination to the scientific community will be implemented.

Lorenzo Bianchi – INFN TORINO