On duality between Cosserat elasticity and fractons
arXiv:1908.06984 · doi:10.21468/SciPostPhys.8.4.065
Abstract
We present a dual formulation of the Cosserat theory of elasticity. In this theory a local element of an elastic body is described in terms of local displacement and local orientation. Upon the duality transformation these degrees of freedom map onto a coupled theory of a vector-valued one-form gauge field and an ordinary gauge field. We discuss the degrees of freedom in the corresponding gauge theories, the defect matter and coupling to the curved space.
16 pages
References in corpus (10)
- Local stabilizer codes in three dimensions without string logical operators
- A Duality Web in 2+1 Dimensions and Condensed Matter Physics
- Towards classification of Fracton phases: the multipole algebra
- Crystallography on Curved Surfaces
- Crystal-to-Fracton Tensor Gauge Theory Dualities
- Correlation function diagnostics for type-I fracton phases
- Fractons from vector gauge theory
- A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
- Two-dimensional melting via sine-Gordon duality
- Elasticity in Curved Topographies: Exact Theories and Linear Approximations
Cited by in corpus (33)
- Fracton hydrodynamics
- Hydrodynamics of ideal fracton fluids
- Hydrodynamics of dipole-conserving fluids
- Simple views on symmetries and dualities in the theory of elasticity
- Odd Cosserat elasticity in active materials
- Effective field theories for gapless phases with fractons via a coset construction
- Dual gauge theory formulation of planar quasicrystal elasticity and fractons
- A symmetry principle for gauge theories with fractons
- Emergent Dipole Gauge Fields and Fractons
- Covariant fracton gauge theory with boundary
- Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
- Fracton-elasticity duality in twisted moiré superlattices
- Fracton gravity from spacetime dipole symmetry
- Tearing Fractons
- Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
- Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
- Bose-Hubbard realization of fracton defects
- Fractalizing quantum codes
- An action for nonlinear dislocation dynamics
- Fracton-elasticity duality on curved manifolds
- Dissipative fracton superfluids
- Elastic Liénard-Wiechert potentials of dynamical dislocations from tensor gauge theory in 2+1 dimensions
- Fractons in effective field theories for spontaneously broken translations
- On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
- Quasi-topological fractons: a 3D dipolar gauge theory
- A geometric formulation of Schaefer's theory of Cosserat solids
- Quadrupole gauge theory: anti-Higgs mechanism and elastic dual
- Fractons on the edge
- Covariant field theory of 3D massive fractons
- Non-equilibrium charge-vortex duality
- Defects in Wigner crystals: fracton-elasticity duality and vacancy proliferation
- Effective field theory for the superfluid vortex lattice from coset construction
- Emergent fracton strings from covariant bi-form gauge field theory