Spontaneous symmetry breaking in free theories with boundary potentials

Abstract

Patterns of symmetry breaking induced by potentials at the boundary of free O(N)O(N)-models in d=3- \epsilond=3−ϵ dimensions are studied. We show that the spontaneous symmetry breaking in these theories leads to a boundary RG flow ending with N - 1N−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 \epsilonϵ-expansion we test these ideas in an O(N)\oplus O(N)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.

Spontaneous symmetry breaking on surface defects

“…5 In theories with moduli spaces it is also possible to induce symmetry breaking in the bulk introducing a potential on the defect, see e.g. [45] for examples in a free scalar theory. In this work we focus on the setup in which the vanishing boundary conditions at infinity preserve the symmetry.…”

“…The existence of surface defects spontaneously breaking a symmetry in a theory with moduli spaces is not that surprising after all. Indeed, in the presence of flat directions in the potential it is possible to construct symmetric defects which lead to standard SSB in the bulk [45], i.e. for which bulk operators acquire a constant expectation value.…”