We continue the exploration of nonstandard continuum field theories related to fractons in 3+1 dimensions. Our theories exhibit exotic global and gauge symmetries, defects with restricted mobility, and interesting dualities. Depending on the model, the defects are the probe limits of either fractonic particles, strings, or strips. One of our models is the continuum limit of the plaquette Ising lattice model, which features an important role in the construction of the X-cube model.

中文翻译：

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3 + 1维度上的更多奇异领域理论

我们将继续探索与3 + 1维分数维相关的非标准连续场理论。我们的理论显示出奇异的全局和规范对称性，活动受限的缺陷以及有趣的对偶性。根据模型的不同，缺陷是分数粒子，细线或条带的探测极限。我们的模型之一是金属板伊辛晶格模型的连续极限，它在X立方体模型的构造中具有重要作用。