Late time behavior of n-point spectral form factors in Airy and JT gravities

Abstract

We study the late time behavior of n-point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, which includes both Airy and JT gravities as special cases. This is conducted in the small ħ expansion, where hbar sim {e}^{-1/{G}_{textrm{N}}} is the genus counting parameter and nonperturbative in Newton’s constant GN. For one-point SFF, we study its absolute square at two different late times. We show that it decays by power law at t ~ ħ−2/3 while it decays exponentially at t ~ ħ−1 due to the higher order corrections in ħ. We also study general n(≥2)-point SFFs at t ~ ħ−1 in the leading order of the ħ expansion. We find that they are characterized by a single function, which is essentially the connected two-point SFF and is determined by the classical eigenvalue density ρ0(E) of the dual matrix integral. These studies suggest that qualitative behaviors of n-point SFFs are similar in both Airy and JT gravities, where our analysis in the former case is based on exact results.