Loop Models, Modular Symmetry and Duality

We will discuss the connection between loop mopdels of particle-hole invariant theories of anyons to field theoreric dualities. We will discuss both systems in two space dimensions and boundaries of 3D systems, and the role of quantum anomalies. We will discuss the signifcance of our results to theories of quantum phase transitions in fractional quantum Hall fluids and other two and three-dimensional topological fluids.