  Loop models have been widely studied in physics and mathematics, in problems
ranging from polymers to topological quantum computation to Schramm-Loewner
evolution. I present new loop models which have critical points described by
conformal field theories. Examples include both fully-packed and dilute loop
models with critical points described by the superconformal minimal models and
the SU(2)_2 WZW models. The dilute loop models are generalized to include
SU(2)_k models as well.
