耦合物质场的量子双子模型：对偶化过程的详细综述
Quantum Double Models coupled to matter fields: a detailed review for a dualization procedure
AI总结：
本文基于Kitaev量子双子模型推广形式的对偶化过程，提出通过格点面添加qudit、规范群余作用同态耦合的新格点规范模型，揭示其准粒子禁闭特性，并指出其可视为2-格点规范理论的二维限制。
摘要：
本文研究了如何基于Kitaev量子双子模型（Kitaev Quantum Double Models）先前推广形式的对偶化过程，定义一类新的格点规范模型。作为基础的先前推广模型，是通过在格点顶点处添加新的qudit（参考部分工作将其记为物质场）来定义的，例如可将这类模型解释为耦合Potts模型的Kitaev量子双子模型。而本文研究的推广形式被定义为上述先前推广形式的对偶，其中这些新的qudit被添加到格点面上。先前推广形式中规范qudit与物质qudit之间的耦合通过规范群作用实现，本文表明，两种推广形式的对偶特性，是通过在第二种推广形式中借助规范群余作用同态耦合这些相同的qudit来达成的。两种推广形式最显著的对偶特征之一是：当上述作用和余作用非平凡时，两者中部分继承自Kitaev量子双子模型的准粒子都会发生禁闭。但本文的重要新发现在于：定义该规范群余作用的群同态不仅可以对第二种推广形式的所有不同模型进行分类，还表明所有这些模型都可解释为2-格点规范理论的二维限制。
英文摘要：
In this paper, we investigate how it is possible to define a new class of lattice gauge models based on a dualization procedure of a previous generalization of the Kitaev Quantum Double Models. In the case of this previous generalization that will be used as a basis, it was defined by adding new qudits (which were denoted as matter fields in reference to some works) to the lattice vertices with the intention of, for instance, interpreting its models as Kitaev Quantum Double Models coupled with Potts ones. Now, with regard to the generalization that we investigate here, which we want to define as the dual of this previous one, these new qudits were added to the lattice faces. And as the coupling between gauge and matter qudits of the previous generalization was performed by a gauge group action, we show that the dual behaviour of these two generalizations was achieved by coupling these same qudits in the second one through a gauge group co-action homomorphism. One of the most striking dual aspects of these two generalizations is that, in both, part of the quasiparticles that were inherited from the Kitaev Quantum Double Models become confined when these action and co-action are non-trivial. But the big news here is that, in addition to the group homomorphism (that defines this gauge group co-action) allows us to classify all the different models of this second generalization, this same group homomorphism also suggests that all these models can be interpreted as two-dimensional restrictions of the $ 2 $-lattice gauge theories.
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