Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations

Abstract

Collective excitations of Fractional Quantum Hall (FQH) liquids at long wavelengths are thought to be of a generally covariant geometric nature, governed by area-preserving diffeomorphisms ($\mathrm{SDiff}$). But current analyses rely solely on the corresponding perturbative $w_{\infty }$ Lie algebra. We argue this is insufficient: We identify a non-perturbative construction of the effective Maxwell-Chern-Simons quantum field theory which carries unitary $\mathrm{SDiff}$ equivariance. But this turns out to be non-differentiable, suggesting underappreciated subtleties when the usual Hilbert space truncation is removed.

7 pages, 1 table; v2 (published version): further discussion added to §II.C

References in corpus (1)

• Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems