Extended Nappi-Witten Geometry for the Fractional Quantum Hall Effect

Abstract

Motivated by the recent progresses in the formulation of geometric theories for the fractional quantum Hall states, we propose a novel non-relativistic geometric model for the Laughlin states based on an extension of the Nappi-Witten geometry. We show 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 from a single Chern-Simons theory with a gauge connection that takes values in the extended Nappi-Witten algebra. We then provide a new derivation of the chiral boson associated to the gapless edge states from the Wess-Zumino-Witten model that is induced by the Chern-Simons theory on the boundary.

arXiv comment5 pages

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Cited by in corpus (6)

• Non-relativistic and Ultra-relativistic Expansions of Three-dimensional Spin-3 Gravity Theories
• Non-Relativistic Supergeometry in the Moore-Read Fractional Quantum Hall State
• The Holographic c-theorem and Infinite-dimensional Lie Algebras
• Non-relativistic spin-3 symmetries in 2+1 dimensions from expanded/extended Nappi-Witten algebras
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• Massive Higher-Spin Fields in the Fractional Quantum Hall Effect