Two-point density-of-states beyond the Airy regime in JT gravity

Determine the form of the averaged connected two-point function of the density of states, \overline{\rho(E1)\rho(E2)}, in JT gravity for energies beyond the universal Airy regime, in order to evaluate thermofield-double length observables at lengths much larger than e^{S0/3}.

Background

In the regime ℓ ∼ e^{S0/3}, the universal Airy kernel controls the two-point function of the density of states, enabling precise evaluations of length observables. However, for larger ℓ, contributions from energies outside the Airy window dominate, and the Airy kernel is no longer applicable.

The authors emphasize that this two-point function outside the Airy regime is currently unknown, which obstructs a complete nonperturbative analysis of time-dependent length expectation values in the thermofield double state.