This dissertation studies defects — things like boundaries, impurities, or probe particles placed inside many-body systems — and asks when their long-distance behavior is universal. "Universal" means that very different microscopic setups can show the same large-scale physics. The author uses symmetry principles to find general statements about defect dynamics across a range of models, from high-energy gauge theories to cold atomic gases.

The work brings together three main themes. First, it analyzes Renormalization Group (RG) flows for defects. An RG flow describes how a system looks when you zoom out to larger length scales. The dissertation studies special fixed points of these flows where defects enjoy extra symmetry, in particular conformal symmetry (scale and angle symmetry), and it derives constraints on defect behavior in those cases. Second, it treats defects as effective strings in contexts related to confined flux tubes and baryon junctions, using ideas such as open–closed duality to control interactions. Third, it applies defect ideas to nonrelativistic systems, developing scale-invariant defect theory for Schrödinger-symmetric models and studying point impurities and giant vortices in rotating superfluids.

Concrete examples appear throughout. The author examines conformal defects and bulk-to-defect operator expansions, constraints on defect-correlators in Maxwell electrodynamics including twist defects tied to electromagnetic duality, and defect phase diagrams in O(N) Wilson–Fisher models where monotonicity and a defect central charge are discussed. In the stringy context, the dissertation analyzes baryon junctions and the leading scattering of large glueball excitations. For atomic gases, it relates point-like impurities to many-body states in a harmonic trap and considers s-wave resonances in dilute Fermi gases; it also studies macroscopic defects called giant vortices in rotating superfluids.