Higher-spin non-relativistic geometry in the fractional quantum Hall effect

Motivated by recent progress in the formulation of geometric modls for the fractional quantum Hall states, we propose a novel non-relativistic geometric model for Laughlin states based on an extension of the Nappi-Witten algebra. We show that, staring from a single Chern-Simons theory with a gauge connection that takes values in the extended Nappi-Witten algebra, that the U(1) gauge sector responsible for the fractional Hall conductance, the gravitational Chern-Simons action and Wen-Zee term associated to the Hall viscosity can be derived in a unified way. When considering the Wess-Zumino-Witten model induced at the boundary, we reproduce the Florianini-Jackiw chiral boson action associated to gapless edge states. By means of a contaction procedure applied to the sl(3,R) algebra, two different higher-spin extension of the Nappi-Witten symmetry are defined. The corresponding Chern-Simons actions extend the previous results to include higher spin fields. The relation between these higher spin exitations and the W-infinity symmetry of quantum incompressible fluids previously considered in the literature by A. Capelli is studied. Generalisation of there results to include non-topological terms in the action are also considered.