Symmetry breaking and RG flows with higher dimensional operators

Abstract: We discuss the role of higher dimensional operators in the spontaneous breaking of internal symmetry and scale invariance, in the context of the Lorentz invariant scalar field theory. Using the $\varepsilon$-expansion we determine phase diagrams and demonstrate that (un)stable RG flows computed with a certain basis of dimension 6 operators in the Lagrangian, map to (un)stable RG flows of another basis related to the first by field redefinitions. Crucial is the presence of reparametrization ghosts if Ostrogradsky ghosts appear.