Bootstrapping perturbative and non-perturbative defect correlators

This proceeding covers results presented at the European network for Particle physics, Lattice field theory and Extreme computing (EuroPLEx2023) conference in Berlin in September 2023. Holographic Wilson lines and defects are studied and reviewed through the complimentary lenses of the analytical conformal bootstrap and the lattice formulation of the gauge-fixed string action. In the first approach, the constraints coming from superconformal symmetry along with minimal additional input are used to fix perturbative correlators of insertions on Wilson lines at strong coupling. In the second, the holographic dual of a Wilson line is considered. The worldsheet formulation of type IIB string theory is discretised in an attempt to describe the system non-perturbatively while preserving the most symmetry possible and matching perturbative computations in the continuum. The overlap and interplay of the methods are discussed.