Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
Supersymmetric Sachdev-Ye-Kitaev models
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Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
Exact BPS spectra for tr(Ψ^p) matrix models at p=5,7 and small N factor as p^k x^{q_min} (1+x)^N times palindromic polynomial, with mod-p index floors bounding large-N growth between log(2 cos(π/2p)) and log 2.
Numerical confirmation that SYK models reproduce RMT spectral edge statistics, yielding power-law quenched entropy at low T and enabling large-N entanglement entropy calculations for supersymmetric wormholes.
Reviews the FL* theory for cuprates using ancilla layer models and SU(2) gauge theories to explain pseudogap hole pockets of area p/8, Fermi arcs, and transitions to d-wave superconductivity and Fermi liquid behavior.
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Chaos of Berry curvature for BPS microstates
Berry curvature of BPS states is random-matrix-like for supersymmetric black hole microstates but non-random and often zero for horizonless geometries, offering a chaos diagnostic in degenerate sectors.
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Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model
Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
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BPS spectra of $\operatorname{tr}[\Psi^p]$ matrix models for odd $p$
Exact BPS spectra for tr(Ψ^p) matrix models at p=5,7 and small N factor as p^k x^{q_min} (1+x)^N times palindromic polynomial, with mod-p index floors bounding large-N growth between log(2 cos(π/2p)) and log 2.
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Exploring the Spectral Edge in SYK Models
Numerical confirmation that SYK models reproduce RMT spectral edge statistics, yielding power-law quenched entropy at low T and enabling large-N entanglement entropy calculations for supersymmetric wormholes.
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Fractionalized Fermi liquids and the cuprate phase diagram
Reviews the FL* theory for cuprates using ancilla layer models and SU(2) gauge theories to explain pseudogap hole pockets of area p/8, Fermi arcs, and transitions to d-wave superconductivity and Fermi liquid behavior.