Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum
arXiv:2303.04479 · doi:10.21468/SciPostPhys.16.2.051
Abstract
We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu--Goldstone modes of higher-form symmetries.
arXiv comment32 pages, 2 figures; v2: expanded discussion and updated reference list; v3: minor revision and further update of the reference list
References in corpus (51)
- Generalized Global Symmetries
- Fractons
- Generalized Symmetries in Condensed Matter
- Fracton Phases of Matter
- Magnon-skyrmion scattering in chiral magnets
- Nonrelativistic effective Lagrangians
- An Introduction to Spontaneous Symmetry Breaking
- Axial anomaly and magnetism of nuclear and quark matter
- Fermions in the Lowest Landau Level: Bosonization, Algebra, Droplets, Chiral Boson
- Towards classification of Fracton phases: the multipole algebra
- Fractons, dipole symmetries and curved spacetime
- Chiral Topological Elasticity and Fracton Order
- Transverse force on a quantized vortex in a superfluid
- On the number of Nambu-Goldstone bosons and its relation to charge densities
- Generalized Bloch theorem and chiral transport phenomena
- The Magnus Force on Skyrmions in Ferromagnets and the Quantum Hall Effect
- Effective Lagrangian for Nonrelativistic Systems
- Anomalous Hydrodynamics of Two-Dimensional Vortex Fluid
- Counting Rules of Nambu-Goldstone Modes
- Higher-form symmetries and 3-group in axion electrodynamics
- Chiral Soliton Lattice and Charged Pion Condensation in Strong Magnetic Fields
- Goldstone modes and photonization for higher form symmetries
- Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
- Meson Supercurrent State in High Density QCD
- An Introduction to Higher-Form Symmetries
- Non-Boost Invariant Fluid Dynamics
- Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
- Invariant Effective Actions, Cohomology of Homogeneous Spaces and Anomalies
- Fracton-elasticity duality of two-dimensional superfluid vortex crystals: defect interactions and quantum melting
- Introduction to Generalized Global Symmetries in QFT and Particle Physics
- Conserved momenta of a ferromagnetic soliton
- Anomalous electrodynamics of neutral pion matter in strong magnetic fields
- Spontaneous Superfluid Current Generation in CFL at Nonzero Strange Quark Mass
- Counting Nambu-Goldstone modes of higher-form global symmetries
- Effective Lagrangians for quantum many-body systems
- Noncommuting Momenta of Topological Solitons
- Meson current in the CFL phase
- Axion electrodynamics and nonrelativistic photons in nuclear and quark matter
- Effective field theories for gapless phases with fractons via a coset construction
- On the Current Carried by `Neutral' Quasiparticles
- A symmetry principle for gauge theories with fractons
- Ideal fracton superfluids
- Goldstone boson currents in a kaon condensed CFL phase
- Axion crystals
- Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
- Some topological issues for ferromagnets and fluids
- On anomalies in classical dynamical systems
- Topological Terms and Diffeomorphism Anomalies in Fluid Dynamics and Sigma Models
- Conserved momenta of ferromagnetic solitons through the prism of differential geometry
- Vortex flows on closed surfaces
- Some useful operators on differential forms in Galilean and Carrollian spacetimes