Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
arXiv:2112.14339 · doi:10.1103/PhysRevD.106.065020
Abstract
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as the neutral collective mode that characterizes the Moore-Read state. By integrating out this fermion field, we obtain a purely bosonic topological action that properly encodes the Hall conductivity, Hall viscosity and gravitational anomaly. Our work paves the way to the exploration of the fractional quantum Hall effect through non-relativistic supergeometry.
arXiv comment7 pages, details added, typos corrected
References in corpus (71)
- Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
- The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
- Viscosity of Quantum Hall Fluids
- A WZW model based on a non-semi-simple group
- Hall Viscosity and Electromagnetic Response
- The exotic Galilei group and the "Peierls substitution"
- Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
- Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity
- A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
- Infinite Symmetry in the Quantum Hall Effect
- Fractional Quantum Hall Effect via Holography: Chern-Simons, Edge States, and Hierarchy
- Spacetime Symmetries of the Quantum Hall Effect
- Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
- Electromagnetic and gravitational responses of two-dimensional non-interacting electrons in background magnetic field
- Fermions in the Lowest Landau Level: Bosonization, Algebra, Droplets, Chiral Boson
- Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
- Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
- Expanding Lie (super)algebras through abelian semigroups
- Fractional Quantum Hall Effect in a Curved Space: Gravitational Anomaly and Electromagnetic Response
- Fractional Quantum Hall Hierarchy and the Second Landau Level
- Low-energy effective theory in the bulk for transport in a topological phase
- Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect
- Density-curvature response and gravitational anomaly
- On Schrödinger superalgebras
- ABJM with Flavors and FQHE
- Bimetric Theory of Fractional Quantum Hall States
- Three-Dimensional Extended Bargmann Supergravity
- Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
- Nonsemisimple Sugawara Constructions
- Newton-Cartan Supergravity
- Geometry of Fractional Quantum Hall Fluids
- Boundary effective action for quantum Hall states
- Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
- Flat space holography and complex SYK
- Chiral Gravitons in Fractional Quantum Hall Liquids
- Geometric adiabatic transport in quantum Hall states
- A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions
- Spectral Sum Rules and Magneto-Roton as Emergent Graviton in Fractional Quantum Hall Effect
- FQHE on curved backgrounds, free fields and large N
- Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
- Investigating anisotropic quantum Hall states with bi-metric geometry
- Neutral Fermion Excitations in the Moore-Read state at ν=5/2
- Geometric quench and nonequilibrium dynamics of fractional quantum Hall states
- On free Lie algebras and particles in electro-magnetic fields
- Numerical Calculation of the Neutral Fermion Gap at
- Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra
- Fractional quantum Hall systems near nematicity: bimetric theory, composite fermions, and Dirac brackets
- Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
- The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
- Enlarged Galilean symmetry of anyons and the Hall effect
- Three-Dimensional Extended Lifshitz, Schrödinger and Newton-Hooke Supergravity
- Galilean invariance at quantum Hall edge
- Multipole Expansion in the Quantum Hall Effect
- Holographic correspondence in topological superconductors
- Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?
- Super-Galilei Invariant Field Theories in 2+1 Dimensions
- Three-dimensional non-relativistic extended supergravity with cosmological constant
- Gravity and the spin-2 planar Schroedinger equation
- The Non-Relativistic Superparticle in a Curved Background
- Boundary central charge from bulk odd viscosity - chiral superfluids
- Galilean Exotic Planar Supersymmetries and Nonrelativistic Supersymmetric Wave Equations
- Collective excitations at filling factor 5/2: The view from superspace
- Non-Abelian Chern-Simons Theory from a Hubbard-like Model
- BF-theory in graphene: a route toward topological quantum computing?
- Four-dimensional black hole entropy from F-theory
- Supersymmetry in the Fractional Quantum Hall Regime
- Physical stress, mass, and energy for non-relativistic matter
- Geometric responses of the Pfaffian state
- Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect
- Field theory of spin-singlet quantum Hall states
- From topological to topologically massive gravity through the gauge principle
Cited by in corpus (8)
- Supergravity model of the Haldane-Rezayi fractional quantum Hall state
- Signatures of Supersymmetry in the Fractional Quantum Hall Effect
- Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
- Noncommutative Geometry and Deformation Quantization in the Quantum Hall Fluids with Inhomogeneous Magnetic Fields
- Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
- Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
- Massive Higher-Spin Fields in the Fractional Quantum Hall Effect
- A note on the Hamiltonian structure of transgression forms