标题： 格子平移调制对称性和拓扑场论 显示英文标题

标题： Lattice Translation Modulated Symmetries and TFTs

摘要： 调制对称性是内部对称性，在时空对称性作用下不保持不变。 我们提出了一种通用的方法，通过张量网络语言来描述1+1D中的晶格平移调制对称性，包括不可逆的对称性。 我们证明了调制可以通过范畴的一些自等价来描述。 尽管由于调制的存在，拓扑行为被破坏，但我们仍然可以通过插入由可逆双模范畴描述的一系列域墙来构建调制对称性的对称性拓扑场论体。 这种结构不仅恢复了一些关于可逆调制对称性的已知结果，还提供了一个通用框架，在更一般的设置中处理调制对称性。 显示英文摘要

摘要： Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the tensor network language. We demonstrate that the modulations can be described by some autoequivalences of the categories. Although the topological behaviors are broken because of the presence of modulations, we can still construct the modulated version of the symmetry TFT bulks by inserting a series of domain walls described by invertible bimodule categories. This structure not only recovers some known results on invertible modulated symmetries but also provides a general framework to tackle modulated symmetries in a more general setting.