arXiv 2012.007012020-12-01hep-thcond-mat.str-el

具有边界势的自由理论中的自发对称性破缺

Spontaneous symmetry breaking in free theories with boundary potentials

Vladimír Procházka, Alexander Söderberg

备注：: 17 pages, 3 figures + Mathematica notebook included
DOI：: 10.21468/SciPostPhys.11.2.035

摘要：

研究了$d=3- ε$维自由$O(N)$模型边界上的势诱导对称性破缺的模式。我们发现，在这些理论中的自发对称性破缺导致边界RG流结束与$N - 1$ Neumann模式的IR。波动引起的对称性破缺的可能性进行了检查，我们推导出一个通用的计算公式在边界处的单圈有效势。使用$ε-$扩展，我们测试这些想法在一个$O(N)\oplus O(N)$模型与边界相互作用。我们确定了该理论的RG流图，发现它有一个满足共形边界条件的IR稳定临界点。计算了有效势的领先修正，并论证了存在一个相边界，该相边界将流向对称不动点的区域与流向非对称破碎相的区域分开，并结合了Neumann和Dirchlet边界条件。

英文摘要：

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