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Chiral Topological Elasticity and Fracton Order
1Brown Theoretical Physics Center and Department of Physics, Brown University, Providence, Rhode Island 02912, USA.
Physical Review Letters
|March 9, 2019
Summary
We introduce a new geometric theory that resolves gauge invariance issues in higher rank gauge theories, capturing fracton order phenomenology. This theory, based on Riemann-Cartan geometry, suggests fracton order is inherently geometric.
Area of Science:
- Theoretical Physics
- Condensed Matter Physics
- Geometric Field Theory
Background:
- Higher rank gauge theories exhibit fracton order phenomenology.
- These theories lack gauge invariance under smooth curvature perturbations.
Purpose of the Study:
- To resolve the gauge invariance problem in higher rank gauge theories.
- To develop a geometric theory capturing fracton phenomenology.
Main Methods:
- Introducing a theory invariant under area-preserving diffeomorphisms.
- Linearizing around a flat background to recover higher rank gauge transformations.
- Utilizing Riemann-Cartan geometry for theory formulation.
Main Results:
- The proposed theory is invariant under area-preserving diffeomorphisms.
- It exhibits fracton phenomenology, including conservation laws and topological excitations.
- The theory is interpreted as chiral topological elasticity.
Conclusions:
- Fracton order phenomenology can be captured by a geometric theory.
- Riemann-Cartan geometry inherently encodes aspects of fracton order.
- The proposed theory offers a resolution to gauge invariance issues in higher rank theories.
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