Abstract
We review the recent progress in the study of line defects in three-dimensional Chern–Simons-matter superconformal field theories, notably the ABJM theory. The first part is focused on kinematical defects, supporting a topological sector of the theory. After reviewing the construction of this sector, we concentrate on the evaluation of topological correlators from the partition function of the mass-deformed ABJM theory and provide evidence on the existence of topological quantum mechanics living on the line. In the second part, we consider the dynamical defects realized as latitude BPS Wilson loops for which an exact evaluation is available in terms of a latitude Matrix Model. We discuss the fundamental relation between these operators, the defect superconformal field theory and bulk physical quantities, such as the Bremsstrahlung function. This relation assigns a privileged role to BPS Wilson operators, which become the meeting point for three exact approaches: localization, integrability and conformal bootstrap.
Highlights
The study of quantum field theories with defects is of crucial importance because they can be used to describe real physical systems that exhibit lower dimensional interplays or doping defects, and because defect theories have proved to be an efficient tool for investigating physical properties of the bulk system itself
We have reviewed some recent progress in the study of line defects in the threedimensional N = 6 ABJM theory
We have considered kinematical defects, that is, trivial one-dimensional submanifolds, which support a topological sector of the theory
Summary
The study of quantum field theories with defects is of crucial importance because they can be used to describe real physical systems that exhibit lower dimensional interplays or doping defects, and because defect theories have proved to be an efficient tool for investigating physical properties of the bulk system itself. This becomes even more efficient when (super)conformal invariance is at work. These are BPS operators corresponding to generalized connections, which include parametric (latitude) couplings to the bosonic and fermionic matter sectors of the theory. A list of interesting open problems that need further investigation is reported there
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