JT gravity in a box is quantized exactly by recasting its dynamics as Pöschl-Teller scattering, producing closed-form wavefunctions and correlators with finite-cutoff corrections beyond T Tbar.
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Looking at supersymmetric black holes for a very long time
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The DSSYK model emerges as the dynamics on the quantum homogeneous space of the von Neumann algebraic quantum group SU_q(1,1) ⋊ Z2.
Develops a constrained particle-on-group formulation of super-JT gravity that yields super-Schwarzian actions, physical supercharges, and explicit N=2/N=4 three-point functions plus zero-energy OTOCs.
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.
In double-scaled SYK, state-adapted dressed chord operators change the emergent algebra from Type II1 to Type I∞ and restore purity of KM states, unlike generic operators.
Summing non-perturbative contributions in the gravitational path integral, extended via matrix integral saddles including one- and two-eigenvalue instantons, resolves negativity of bulk entropies in two-sided black holes.
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.
Finite-N non-planar mixing in the D1D5 CFT produces level repulsion and random-matrix statistics in symmetry-resolved sectors, while the planar large-N limit yields Poisson statistics.
Non-planar corrections lift degeneracies in the spectrum of quarter BPS states in Sym^N(T^4) and introduce level repulsion plus random matrix statistics, showing integrability is restricted to the large N planar limit.
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.
A semiclassical construction of fiducial observers in JT gravity, fixed by conformal isometry flow, is extended to the quantum regime to compute wormhole contributions yielding finite thermal entropy and a quantum description of the stretched horizon.
Conjugation deformations preserve normalizability in the BMN matrix model, implying BPS states do not lift and their unsigned number is invariant except at the free and BFSS points.
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.