A symmetry principle for gauge theories with fractons

Abstract

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.

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

“…While we have initially restricted the discussion to d = 2 spatial dimensions, the generalization to higher dimensions is easy. The on-shell relation (9) remains valid for any d. What changes is only the definition of the topological current descending from the symplectic form,…”

“…where e A is the basis of 1-forms, dual to e A . This is the coordinate-free generalization of (9). It remains to combine this with the off-shell conservation of the current (10), which now reads simply d(dω) = 0.…”

“…Physical systems featuring a given multipole symmetry can be constructed using standard symmetry-based techniques of effective field theory (EFT) [8,9]. However, the question in what kind of systems one may actually expect a multipole symmetry does not seem to have a clear answer.…”