LAUSR

We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a SO(7)_{1}/(G_{2})_{1} coset factorization, leads to a solvable one-dimensional model that is extended to two dimensions using a network construction. In addition to providing a description of the Fibonacci phase without parafermions, our theory predicts a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We show that Majorana fermions can split into a pair of Fibonacci anyons, and propose an interferometer that generalizes the Z_{2} Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.