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arXiv · 2012.00701

Spontaneous symmetry breaking in free theories with boundary potentials

Vladimír Procházka·Alexander Söderberg
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Abstract

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 $O(N)\oplus O(N)$ 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.

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Vladimír Procházka, Alexander Söderberg. 2020-12-01. Spontaneous symmetry breaking in free theories with boundary potentials. https://doi.org/10.21468/scipostphys.11.2.035

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