Homoclinic Renormalization Group Flows, or When Relevant Operators Become Irrelevant.

We study an N=1 supersymmetric quantum field theory with O(M)×O(N) symmetry. Working in 3-ε dimensions, we calculate the beta functions up to second loop order and analyze in detail the renormalization group (RG) flow and its fixed points. We allow N and M to assume general real values, which results in them functioning as bifurcation parameters.