Anomalous Continuous Translations
arXiv:2412.14434 · doi:10.21468/SciPostPhys.19.2.031
Abstract
We discuss a large class of non-relativistic continuum field theories where the Euclidean spatial symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry, making it non-Abelian. This presentation streamlines and extends the discussion in [1]. In an Appendix, we present an elementary introduction to 't Hooft and Adler-Bell-Jackiw anomalies using a well-known system.
30 pages, minor changes
References in corpus (37)
- Generalized Global Symmetries
- Coupling a QFT to a TQFT and Duality
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- Is the Composite Fermion a Dirac Particle?
- Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
- Anomalies in the Space of Coupling Constants and Their Dynamical Applications II
- Anomalies in the Space of Coupling Constants and Their Dynamical Applications I
- Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
- Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
- Building crystalline topological phases from lower-dimensional states
- Dual Dirac liquid on the surface of the electron topological insulator
- Gauging spatial symmetries and the classification of topological crystalline phases
- Intrinsic and emergent anomalies at deconfined critical points
- The half-filled Landau level: the case for Dirac composite fermions
- Symmetric-Gapped Surface States of Fractional Topological Insulators
- Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
- Heisenberg Groups and Noncommutative Fluxes
- Lieb-Schultz-Mattis, Luttinger, and 't Hooft -- anomaly matching in lattice systems
- Majorana chain and Ising model -- (non-invertible) translations, anomalies, and emanant symmetries
- A Modified Villain Formulation of Fractons and Other Exotic Theories
- Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
- Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
- Electric polarization as a nonquantized topological response and boundary Luttinger theorem
- Crystalline gauge fields and quantized discrete geometric response for Abelian topological phases with lattice symmetry
- Conserved momenta of a ferromagnetic soliton
- Energy-momentum tensor of a ferromagnet
- Noncommuting Momenta of Topological Solitons
- Non-Invertible Chiral Symmetry and Exponential Hierarchies
- Classification of fractional quantum Hall states with spatial symmetries
- Some topological issues for ferromagnets and fluids
- K-Theory in Quantum Field Theory
- Conserved momenta of ferromagnetic solitons through the prism of differential geometry
- Is Schwinger Model at Finite Density a Crystal?
- Ferromagnets, a New Anomaly, Instantons, and (noninvertible) Continuous Translations
- Gappability Index for Quantum Many-Body Systems
- Non-invertible Global Symmetries in the Standard Model
- Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum