标题： 四极矩规范理论：反希格斯机制和弹性对偶 显示英文标题

标题： Quadrupole gauge theory: anti-Higgs mechanism and elastic dual

摘要： 受弹性与晶格规范理论之间对偶性的启发，我们研究了包含四极矩的规范群扩展。令人惊讶的是，我们发现四极对称性的自发破缺增加了无质量激发的数量。这一结果似乎挑战了广为接受的范式，即规范场通过希格斯机制获得质量，而原本的戈德斯通玻色子被赋予质量。我们将这一现象称为反希格斯机制。此外，在标准处理晶格-弹性对偶性时，为了限制位错沿其伯格斯矢量滑动，四极矩的守恒是人为引入的。我们的研究澄清了弹性对偶理论中四极对称性的起源，表明四极规范理论并非先验地与弹性固体对偶，而是与一类不同的系统对偶，我们将其称为不可压缩晶体。然而我们认为，当四极对称性被希格斯化，并且不可压缩晶体经历相变进入可压缩固态时，普通弹性的现象学可以被恢复。 显示英文摘要

摘要： Motivated by the duality between elasticity and fracton gauge theory, we study an extension of the gauge group that includes the quadrupole moment. Remarkably, we find that spontaneous breaking of the quadrupole symmetry increases the number of massless excitations. This result appears to challenge the well-established paradigm, according to which gauge fields acquire mass through the Higgs mechanism, and the would-be Goldstone bosons are rendered massive. We refer to this phenomenon as the anti-Higgs mechanism. Furthermore, in the standard treatment of the fracton-elasticity duality, the conservation of quadrupole moment is incorporated ad hoc in order to restrict the motion of dislocations to glide along their Burgers vectors. Our study clarifies the origin of the quadrupole symmetry in the dual theory of elasticity, demonstrating that quadrupole gauge theory is not a priori dual to elastic solids but rather to a distinct class of systems, which we dub incompressible crystals. We argue, however, that the phenomenology of ordinary elasticity is recovered after the quadrupole symmetry is Higgsed and an incompressible crystal undergoes a phase transition to a compressible solid state.