论文标题
仪表理论的对称原理
A symmetry principle for gauge theories with fractons
论文作者
论文摘要
分形阶段是物质的新阶段,它们具有受限制的兴奋性。我们表明,由于连续的高格式对称性的自发断裂,其保守的电荷不会与空间翻译通勤。我们将这种对称性称为非均匀的高格式对称性。这些对称性属于量子场理论中较高形式对称性的标准定义,相应的对称发生器是拓扑。粒子的世界线被认为是1形对称的带电对象,并且可以通过引入其他1形式对称器来实现迁移率限制,这些对称的发电机不会以空间翻译的形式通勤。这些特征是通过与自发损坏的非均匀1形式对称性相关的有效场理论实现的。在低能量下,这些理论还原为已知的高级规定理论,例如标量/矢量电荷仪表理论,这些理论中的无间隙激发被解释为nambu-nambu-goldstone模式,用于更高形式的对称性。由于对称性的不均匀性,某些模式获得了一个间隙,这是时空对称性的逆希格斯机理的更高形式的类似物。仪表理论具有新出现的非均匀磁对称性,并且某些磁性单极管变成了分形。我们确定了非均匀形式对称性和相应的体积对称性保护拓扑阶段的't〜hooft异常。通过这种方法,移动性限制是通过选择电荷与翻译的换向关系的完全确定的。这种方法使我们能够从统一的角度查看现有的(无间隙)分形码模型,例如标量/矢量电荷量规及其变体,并使我们能够具有所需的移动性限制的理论。
Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu--Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the 't~Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.