We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincar\'e or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The "gauge structure" can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang-Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle-hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

中文翻译：

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非阿贝尔分形和嵌入的高阶张量场理论

我们在任何维度上制定了一类新的张量规范场理论，它是对称高阶张量规范理论（即高自旋规范理论）和反对称张量拓扑场理论之间的混合类。我们的理论描述了无间隙和有间隙拓扑有序相之间相互作用的混合单一相（它可以存在或不存在欧几里得、庞加莱或各向异性对称性，至少在紫外线高能或中能场理论中，但尚未达到晶格截止规模）。“规范结构”可以是紧凑的、连续的、阿贝尔的或非阿贝尔的。我们的理论在 1865 年的麦克斯韦电磁理论和 1954 年的杨-米尔斯同位旋/颜色理论范式之外。我们根据未测量的类似矢量或类似张量的高矩全局对称性来讨论其局部规范变换。非阿贝尔规范结构是由测量非交换对称性引起的：高矩对称性和电荷共轭（粒子-空穴）对称性。沿时间方向的矢量全局对称性可能表现出时间晶体。我们探索了这些长程纠缠物质与凝聚态物质中 Fracton 阶的非阿贝尔概括、叶理的场论公式、我们新引入的时空嵌入和嵌入，以及可能在暗物质或暗物质中的基本物理应用之间的关系。暗能量。