We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT) since, unlike the X-cube model, TQFTs are invariant (i.e., symmetric) under continuous space-time transformations. However, the theory is instead invariant under a certain subgroup of the conformal group. We describe how braiding statistics and ground-state degeneracy are reproduced by the field theory, and how the the X-cube Hamiltonian and field theory can be minimally coupled to matter fields. We also show that even on a manifold with trivial topology, spatial curvature can induce a ground-state degeneracy that is stable to arbitrary local perturbations! Our formalism may allow for the description of other fracton field theories, where the only necessary input is an equation of motion for a charge density.

中文翻译：

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X立方体分形拓扑拓扑的量子场论和几何的鲁棒退化

我们提出了关于分数维拓扑阶数的X立方模型的量子场理论描述。场论不是（也不能是）拓扑量子场论（TQFT），因为与X立方模型不同，TQFT在连续的时空变换下是不变的（即对称的）。但是，该理论在共形群的某个子群下是不变的。我们描述了场论如何再现编织统计量和基态简并性，以及X立方体哈密顿量和场论如何最小限度地与物质场耦合。我们还表明，即使在具有微不足道拓扑的流形上，空间曲率也会引起对任意局部扰动稳定的基态简并！我们的形式主义可能允许描述其他分形场理论，