We extend our exploration of nonstandard continuum quantum field theories in 2+1 dimensions to 3+1 dimensions. These theories exhibit exotic global symmetries, a peculiar spectrum of charged states, unusual gauge symmetries, and surprising dualities. Many of the systems we study have a known lattice construction. In particular, one of them is a known gapless fracton model. The novelty here is in their continuum field theory description. In this paper, we focus on models with a global $U(1)$ symmetry and in a followup paper we will study models with a global $\mathbb{Z}_N$ symmetry.

中文翻译：

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3 + 1维量子场论中的奇异$ U（1）$对称性，对偶性和分形

我们将2 + 1维的非标准连续谱量子场理论的探索扩展到3 + 1维。这些理论表现出奇异的全局对称性，带电态的奇特谱，不寻常的规范对称性以及令人惊讶的对偶性。我们研究的许多系统都具有已知的晶格结构。特别地，其中之一是已知的无间隙分数模型。这里的新颖之处在于它们的连续场理论描述。在本文中，我们将重点放在具有全局$ U（1）$对称性的模型上，并在后续论文中，我们将研究具有全局$ \ mathbb {Z} _N $对称性的模型。