Adopted JT disk spectral model

Use natural units $c=\mathrm{\hslash }=k_B=1$. Thus energy $E$ has units ${\mathrm{s}}^{-1}$, inverse temperature $\beta$ and the positive model parameter $C$ have units $\mathrm{s}$, and $S_0\in \mathbb{R}$ is dimensionless. In this item, JT disk model means only the disk-sector spectral model with the density specified below; the label refers to the cited two-dimensional Jackiw–Teitelboim calculations and adopts no additional field equation or path-integral construction. Genus-zero disk contribution means the single connected disk term, with one boundary and no handles, in the formal expansion by spacetime topology. A nonperturbative completion means additional exact model data that select an exact theory beyond the terms fixed by that formal expansion.

A continuous spectral density here is a nonnegative function ${\rho }_0:(0,\mathrm{\infty })\to [0,\mathrm{\infty })$ whose measure ${\rho }_0(E)dE$ assigns model spectral weight to energy intervals. Adopt

${\rho }_0(E):=e^{S_0}\frac{C}{2{\pi }^2}\sinh \text{\hspace{0.17em}⁣}\left(2\pi \sqrt{2CE}\right),E>0.$

The density has units $\mathrm{s}$, so ${\rho }_0(E)dE$ is dimensionless. This postulate specifies a continuous disk-level input only. It does not specify an individual discrete energy spectrum, sum higher-topology terms, choose a nonperturbative completion, or assert that the model describes nature.

Phil Saad, Stephen H. Shenker, and Douglas Stanford, JT gravity as a matrix integral

Thomas G. Mertens and Gustavo J. Turiaci, Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity

Gábor Sárosi, AdS2 holography and the SYK model

The prior restricted semiclassical AdS entropy dictionary Restricted semiclassical entropy dictionary concerns bulk dimension $d+1$ with $d\ge 2$, and is background context only for this two-dimensional disk model: none of its entropy-dictionary assumptions is adopted here, and it does not derive this disk density. The disk expression remains a separate adopted input; any exact boundary quantum system, higher-genus expansion, or nonperturbative completion is outside this postulate.