Fixed lines in four fermion models in two dimensions

Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of $N$ free fermions. Through two loops we find a new class of models, apart from the well-known Abelian Thirring models. Further study is needed to see whether these can lead to true conformal manifolds, or perhaps a new class of large N fixed points.