Title: Topology and strong four fermion interactions in four dimensions,
Abstract: We study massless fermions interacting through a particular four fermion term
in four dimensions. Exact symmetries prevent the generation of bilinear fermion
mass terms. We determine the structure of the low energy effective action for
the auxiliary field needed to generate the four fermion term and find it has an
novel structure that admits topologically non-trivial defects with non-zero
Hopf invariant. We show that fermions propagating in such a background pick up
a mass without breaking symmetries. Furthermore pairs of such defects
experience a logarithmic interaction. We argue that a phase transition
separates a phase where these defects proliferate from a broken phase where
they are bound tightly. We conjecture that by tuning one additional operator
the broken phase can be eliminated with a single BKT-like phase transition
separating the massless from massive phases.