Foundations

The presence of conformal symmetry imposes significant constraints on the observables of a conformal field theory, making this class of models more tractable compared to general quantum field theories while retaining key features. Conformal defects provide a way to break conformal symmetry in a controlled manner. They introduce non-trivial boundary conditions on the fields that give rise to new interesting physical phenomena. Despite this symmetry breaking, correlation functions associated with defects remain highly constrained, occasionally allowing exact results to be derived. This chapter serves as an introduction to line defects in conformal field theories. We review how the correlation functions of a bulk theory are impacted by the presence of a defect, and how the residual symmetry can be used to derive results in both the weak- and strong-coupling regimes. Our focus lies on two distinct classes of models: \({\mathcal {N}}=4\) Super Yang-Mills with a supersymmetric Wilson-line defect, and Yukawa CFTs in the presence of a magnetic line.