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arXiv · 2602.02292

Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations

Hisham Sati·Urs Schreiber
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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.

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Hisham Sati, Urs Schreiber. 2026-02-02. Non-Perturbative SDiff Covariance of Fractional Quantum Hall Excitations. https://doi.org/10.1209/0295-5075%2Fae57d7

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