论文标题
边界RG流量为费米子和mod 2异常
Boundary RG Flows for Fermions and the Mod 2 Anomaly
论文作者
论文摘要
d = 1+1尺寸的Majorana费物的边界条件落入了与MOD 2异常相关的两个SPT相中的一个。在这里，我们考虑了保留$ u（1）^n $对称性的2N Majorana fermions的边界条件。通常，在这种对称性下，左移动和右移动费用具有不同的费用，边界条件的实施需要新的自由度，这表现在边界中央费用$ g $中。 我们遵循通过打开相关边界运算符引起的边界RG流。我们确定红外边界状态。在许多情况下，边界状态将SPT类翻转，导致取消异常需要的新兴Majorana模式。我们表明，UV和IR边界中央电荷的比率由$ g^2_ {ir} / g^2_ {uv} = {\ rm dim} \，（{\ cal o}）$，扰动边界操作员的维度。任何相关操作员都必须具有$ {\ rm dim}（{\ cal o}）<1 $，以确保中央电荷按照G理论的一致。
Boundary conditions for Majorana fermions in d=1+1 dimensions fall into one of two SPT phases, associated to a mod 2 anomaly. Here we consider boundary conditions for 2N Majorana fermions that preserve a $U(1)^N$ symmetry. In general, the left-moving and right-moving fermions carry different charges under this symmetry, and implementation of the boundary condition requires new degrees of freedom, which manifest themselves in a boundary central charge, $g$. We follow the boundary RG flow induced by turning on relevant boundary operators. We identify the infra-red boundary state. In many cases, the boundary state flips SPT class, resulting in an emergent Majorana mode needed to cancel the anomaly. We show that the ratio of UV and IR boundary central charges is given by $g^2_{IR} / g^2_{UV} = {\rm dim}\,({\cal O})$, the dimension of the perturbing boundary operator. Any relevant operator necessarily has ${\rm dim}({\cal O}) < 1$, ensuring that the central charge decreases in accord with the g-theorem.
