Spontaneous symmetry breaking in free theories with boundary potentials

• Patterns of symmetry breaking induced by potentials at the boundary of free O(N)models in d = 3 - epsilon 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 epsilon-expansion we test these ideas in an O(N) circle plus O(N)-model with boundary interactions. We determine the RG flow diagram of this theory and find that it has an IRstable 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.

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NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

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