紧拓扑超导体模型的对偶性与Witten效应
Duality of a compact topological superconductor model and the Witten effect
摘要：
考虑了3+1维带拓扑轴子项的紧致阿贝尔Higgs模型，构造了强耦合下体和边界的对偶理论。该模型可以被看作是描述一个超导体的磁单极子，这也可以解释为一个拓扑莫特绝缘体的场论。我们表明，这个模型是一个非紧的粒子和旋涡的拓扑场论的对偶。它与带有轴子项的超导宇宙弦模型具有完全相同的形式。我们认为在强耦合的边界场论的对偶性，并表明，在这种情况下，$θ$是量子化的$-8πn/m$，其中$n$和$m$是量子数与电荷和磁荷。这些拓扑状态缺乏一个非相互作用的等价物。
英文摘要：
We consider a compact abelian Higgs model in 3+1 dimensions with a topological axion term and construct its dual theories for both bulk and boundary at strong coupling. The model may be viewed as describing a superconductor with magnetic monopoles, which can also be interpreted as a field theory of a topological Mott insulator. We show that this model is dual to a non-compact topological field theory of particles and vortices. It has exactly the same form of a model for superconducting cosmic strings with an axion term. We consider the duality of the boundary field theory at strong coupling and show that in this case $θ$ is quantized as $-8πn/m$ where $n$ and $m$ are the quantum numbers associated to electric and magnetic charges. These topological states lack a non-interacting equivalent.
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