Gravity and the spin-2 planar Schroedinger equation
Eric A. Bergshoeff, Jan Rosseel, Paul K. Townsend
TL;DR
This paper derives a novel non-relativistic Schrödinger equation for spin-2 modes in fractional Quantum Hall states from Einstein and Fierz-Pauli equations, revealing a harmonic oscillator potential for spin-2 particles.
Contribution
It introduces a new non-relativistic limit and null reduction approach to connect gravitational field equations with quantum Hall spin-2 excitations.
Findings
Derivation of a Schrödinger equation for spin-2 modes in 2+1 dimensions.
Identification of a harmonic oscillator potential for spin-2 particles.
Connection between Einstein field equations and quantum Hall excitations.
Abstract
A Schroedinger equation proposed for the GMP gapped spin-2 mode of fractional Quantum Hall states is found from a novel non-relativistic limit, applicable only in 2+1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3+1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the non-linear Einstein equations, a confining harmonic oscillator potential for the individual particles.
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