论文标题
具有边界电势的自由理论中的自发对称性破裂
Spontaneous symmetry breaking in free theories with boundary potentials
论文作者
论文摘要
研究了$ d = 3-ε$维度在$ o（n）$模型边界处的电势引起的对称破坏的模式。我们表明，这些理论中的自发对称性破裂导致IR中以$ n -1 $ neumann模式结束的边界RG流。检查了波动引起的对称破裂的可能性，我们得出了计算边界上一环有效电位的一般公式。使用$ε-$扩展，我们在具有边界交互的$ O（n）\ oplus o（n）$模型中测试了这些想法。我们确定该理论的RG流程图，并发现它具有满足共形边界条件的IR稳定临界点。计算了对有效电位的领先校正，我们认为存在一个相边界的存在，该区域将流到对称固定点的区域与流向对称性的区域的对称固定点，并结合了Neumann和Dirchlet边界条件。
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.
