Fitzpatrick, A. LiamCogburn, Cameron Valier2024-10-022024-10-022023https://hdl.handle.net/2144/49366In this thesis we explore CFTs and related nonperturbative phenomena through several various techniques. First we construct a novel way to latticize AdS via the triangle group. We characterize aspects of this tessellation in 2d as well extend the construction to 3d, where we find a bulk critical point for scalar 𝜙⁴ theory. We then study 2d minimal model CFTs in a bulk AdS₂ through powerful boundary CFT and JT/Schwarzian techniques. Finally, we use an algebraic formulation of a conformal interface separating two minimal models -- a RG brane -- to compute correlators in the presence of the brane to better understand the relation between different minimal model CFT theories.en-USAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/PhysicsAdS/CFTConformal field theoryLattice field theoryQuantum field theoryThesis/Dissertation2024-10-010000-0003-0294-4972