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

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 h expansion, where h similar to e(-1/GN) is the genus counting parameter and nonperturbative in Newton's constant G(N). For one-point SFF, we study its absolute square at two different late times. We show that it decays by power law at t similar to h(-2/3) while it decays exponentially at t similar to h(-1) due to the higher order corrections in h. We also study general n(>= 2)-point SFFs at t similar to h(-1) in the leading order of the h 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 rho(0)(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.

Automated summary

We study the late time behavior of n-point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, including both Airy and JT gravities as special cases. For one-point SFF, we find it decays by power law at t similar to h(-2/3) and decays exponentially at t similar to h(-1). We also study general n(>= 2)-point SFFs at t similar to h(-1) and find that they are characterized by a single function determined by the classical eigenvalue density of the dual matrix integral.