Spectral form factor for free large N gauge theory and strings

I will discuss the spectral form factor for free large N gauge theory and highly excited strings, a quantity that has attracted much recent attention in the context of black holes. In these simpler systems, after a rapid early decay, the spectral form factor rises again due to new contributions. In both cases, the spectral form factor can be characterized by quantities that have some "geometrical" flavor. In gauge theories, the "geometries" are various eigenvalue distributions of the thermal holonomy. For a gas of string, the "geometries" are various winding modes on the thermal manifold, or more literally, classical solutions such as the Horowitz-Polchinski solution. The focus will be the new "geometries" responsible for the rise of the spectral form factor. The discussion will be based on arXiv:2202.04741.