The Quantum Hall Effect in Supersymmetric Chern-Simons Theories

Abstract

We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics to a matrix model, show that their ground state wavefunction is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.

31 pages + appendices. 4 Figures. v2: references added and further comments on the chiral edge modes. v3: introduction and abstract rewritten for a condensed matter audience. More references added. Version to be published in Physical Review B

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• Geometric Model of Topological Insulators from the Maxwell Algebra
• A Green's function approach to the linear response of a driven dissipative optomechanical system
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• Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
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• Matrix supergroup Chern-Simons models for vortex-antivortex systems
• Vortex counting and the quantum Hall effect
• Roton-phonon excitations in Chern-Simons matter theory at finite density
• Quantum Algebra of Chern-Simons Matrix Model and Large $N$ Limit