Spontaneous symmetry breaking in free theories with boundary potentials

Abstract

Patterns of symmetry breaking induced by potentials at the boundary of free O(N)models in d = 3 − ε dimensions are studied. We show that the spontaneous symmetry breaking in these theories leads to a boundary RG flow ending with N−1 Neumann modes in the IR. The possibility of fluctuation-induced symmetry breaking is examined and we derive a general formula for computing one-loop effective potentials at the boundary. Using the ε-expansion we test these ideas in an O(N) O(N)-model with boundary interactions. We determine the RG flow diagram of this theory and find that it has an IR-stable critical point satisfying conformal boundary conditions. The leading correction to the effective potential is computed and we argue the existence of a phase boundary separating the region flowing to the symmetric fixed point from the region flowing to a symmetry-broken phase with a combination of Neumann and Dirchlet boundary conditions.