Vacuum misalignment in presence of four-Fermi operators

We consider the issue of vacuum misalignment induced by four-Fermi couplings in a generic strongly coupled four-dimensional gauge theory. After briefly reviewing the general formalism, we focus on the case of partial compositenesslike operators at leading order, which is relevant in applications to phenomenology. We show that the interactions between an elementary fermion and composite spin-1=2 operators in various representations contribute to the effective potential with relative sign differences. Thus the correct sign required to misalign the vacuum is guaranteed to occur for some representations but not all of them. The overall sign dictating the specific representations responsible for misalignment can in principle be determined on the lattice. We also comment on the likely sign for some simple cases.