标题： 具有边界势的自由理论中的自发对称性破缺 显示英文标题

标题： Spontaneous symmetry breaking in free theories with boundary potentials

摘要： 研究了自由模型边界处势诱导的对称性破缺模式，这些模型处于$O(N)$维空间$d=3- \epsilon$维中。我们证明了这些理论中的自发对称性破缺会导致边界RG流最终以$N - 1$个Neumann模式结束于红外区域。我们检验了由涨落引起的对称性破缺的可能性，并推导出一个用于计算边界处单圈有效势的一般公式。利用$\epsilon-$展开，我们在具有边界相互作用的$O(N)\oplus O(N)$模型中测试了这些思想。我们确定了该理论的RG流图，并发现它有一个满足共形边界条件的红外稳定临界点。我们计算了有效势的主要修正，并论证了存在一个相边界，它将流向对称不动点的区域与流向具有Neumann和Dirichlet边界条件的对称破缺相的区域分隔开来。 显示英文摘要

摘要： 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.