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 1form 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. CONTENTSI. Introduction II. Fractons from nonuniform higher-form symmetries A. Nonuniform higher-form symmetries B. Strategy to realize fractons C. Deformation of symmetry generators III. Gauge theory with U (1) and dipole symmetries A. U (1) and dipole symmetries and their gauging B. Gauge theory of U (1) charge-and dipole-gauge fields C. Low energy limit and the relation to the scalar charge gauge theory D. Number of gapless modes E. Higher-form symmetries and fractons F. Dual theory G. SSB of higher-form symmetries H. Extended operators at low energies I. Gauging of nonuniform higher-form symmetries, 't Hooft anomalies, and an SPT action J. Higgsing and fracton order K. Variants of the scalar charge gauge theory IV. Vector charge gauge theory from nonuniform symmetries

Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d + 1 dimensions

“…It would be important to study about excitations in foliated theories and find a correspondence with the theories studied in this paper. Last but not least, there should be various interesting directions in future related to other recent progress [12][13][14][15][44][45][46][47][48][49][50][51][52][53][54].…”

Ideal fracton superfluids

“…This will simultaneously tell us about the background spacetime geometry that fracton field theories couple to and the gauge fields present in the low-energy description, as well as the transformation properties of these fields. "Gauging algebras" [51,52] has a long and illustrious history in the context of non-Lorentzian geometry [53][54][55][56], while complementary approaches involving Lie algebra-valued connections have previously been considered for fractonic theories in [57][58][59][60].…”

“…Using the inverse relations Φ = −v µ B µ and Bµ = h ν µ B ν , this Ward identity reduces to (51) when using the relations between the currents (58). Since the Ward identities (47) are true off-shell, we may impose (60) in (57) leading to the following action variation…”

Lifshitz symmetry: Lie algebras, spacetimes and particles

“…Exotic aristotelian theories with scalar charge By showing that these symmetries exist and can be consistently realised we have provided the first nontrivial step for the construction of exotic aristotelian theories with scalar charge. However, to further clarify their physical relevance and the relation to fracton-like theories it would be interesting to construct field theories that realise these symmetries (e.g., following [54]).…”