论文标题
边界的3D大$ N $矢量模型
3d Large $N$ Vector Models at the Boundary
论文作者
论文摘要
我们考虑一个4D标量场，在3D边界上耦合到Bosonic或Fermionic的大型$ n $或关键$ o（n）$ vector模型。我们计算在大型$ n $扩展中的第一个非平凡订单，正好在耦合中，以经典的边际体积/边界相互作用计算了$β$的函数。从弱耦合处的自由（临界）矢量模型开始，我们在无限耦合处找到一个固定点，其中边界理论是关键（自由）矢量模型和批量decouples。我们表明，强/弱的二元性将重新归一化组的一个描述与另一个相关的描述与交换自由和关键矢量模型的另一个相关。然后，我们考虑了批量上有一个额外的麦克斯韦场的理论，该理论还通过边界上的测量矢量模型给出了脱钩极限。
We consider a 4d scalar field coupled to large $N$ free or critical $O(N)$ vector models, either bosonic or fermionic, on a 3d boundary. We compute the $β$ function of the classically marginal bulk/boundary interaction at the first non-trivial order in the large $N$ expansion and exactly in the coupling. Starting with the free (critical) vector model at weak coupling, we find a fixed point at infinite coupling in which the boundary theory is the critical (free) vector model and the bulk decouples. We show that a strong/weak duality relates one description of the renormalization group flow to another one in which the free and the critical vector models are exchanged. We then consider the theory with an additional Maxwell field in the bulk, which also gives decoupling limits with gauged vector models on the boundary.
