Magic Fermions: Carroll and Flat Bands
arXiv:2211.11640 · doi:10.1007/JHEP03(2023)227
Abstract
The Carroll algebra is constructed as the limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null surfaces. Due to the availability of two different (degenerate) metrics on Carroll spacetimes, there is the possibility of two different versions of Carroll Clifford algebras. We consider both possibilities and construct explicit representations of Carrollian gamma matrices and show how to build higher spacetime dimensional representations out of lower ones. Actions for Carroll fermions are constructed with these gamma matrices and the properties of these actions are investigated. We show that in condensed matter systems where the dispersion relation becomes trivial i.e. the energy is not dependent on momentum and bands flatten out, Carroll symmetry generically appears. We give explicit examples of this including that of twisted bi-layer graphene, where superconductivity appears at so called magic angles and connect this to Carroll fermions.
Five figures, 40+ pages
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Cited by in corpus (32)
- Carrollian Origins of Bjorken Flow
- Carroll black holes
- Carrollian fluids and spontaneous breaking of boost symmetry
- Carroll fermions in two dimensions
- One-Loop Quantum Effects in Carroll Scalars
- Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics
- Quantizing Carrollian field theories
- Super-Carrollian and Super-Galilean Field Theories
- Carrollian Supersymmetry and SYK-like models
- Carrollian Yang-Mills Theory
- Quantization of Carrollian conformal scalar theories
- Circuit Complexity for Carrollian Conformal (BMS) Field Theories
- Symmetry Resolution in non-Lorentzian Field Theories
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- A Carroll Limit of AdS/CFT: A Triality with Flat Space Holography?
- Quantization of Carrollian fermions
- Carroll spinors
- Carroll-Schrödinger Equation
- Supersymmetric Carroll Galileons in Three Dimensions
- Hydrodynamics in the Carrollian regime
- Carroll black holes in (A)dS and their higher-derivative modifications
- Anisotropic conformal Carroll field theories and their gravity duals
- Post-Carrollian Mechanics, Ideal Gas, and Gravity
- Universal sectors of two-dimensional Carrollian CFTs
- Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
- Free-field construction of Carrollian -algebras
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