A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
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Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.
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Hofstadter's Butterfly in AdS$_3$ Black Holes
A single-band lattice model on the BTZ cylinder produces a curvature-dependent Harper equation whose spectra show sharpened butterfly fragmentation at weak curvature and suppressed magnetic response near larger horizons.
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Dimensional reduction of AdS3 Chern-Simons gravity: Schwarzian and affine boundary theories
Symmetry reduction of 3D AdS Chern-Simons gravity on toroidal boundary yields two inequivalent 1D boundary theories: standard Schwarzian and affine-deformed Schwarzian with Kac-Moody extensions.