Sachdev-Ye-Kitaev spectral statistics and the emergent 1D quantum gravity
The SYK model: N Majorana fermions with all-to-all random quartic interactions J_{ijkl}. At low energies it becomes exactly solvable via Schwinger-Dyson equations, with spectral density following a semicircle modified by a "ramp+plateau" (GUE). The Schwarzian action governs soft-mode fluctuations, giving linear-in-T specific heat and maximal quantum chaos (λ_L = 2πT).