  We present a quantitative and fully non-perturbative description of the
ergodic phase of quantum chaos in the setting of two-dimensional gravity. To
this end we describe the doubly non-perturbative completion of semiclassical 2D
gravity in terms of its associated universe field theory. The guiding principle
of our analysis is a flavor-matrix theory (fMT) description of the ergodic
phase of holographic gravity, which exhibits $\mathrm{U}(n|n)$ causal symmetry
breaking and restoration. JT gravity and its 2D-gravity cousins alone do not
realize an action principle with causal symmetry, however we demonstrate that
their {\it universe field theory}, the Kodaira-Spencer (KS) theory of gravity,
does. After directly deriving the fMT from brane-antibrane correlators in KS
theory, we show that causal symmetry breaking and restoration can be understood
geometrically in terms of different (topological) D-brane vacua. We interpret
our results in terms of an open-closed string duality between holomorphic
Chern-Simons theory and its closed-string equivalent, the KS theory of gravity.
Emphasis will be put on relating these geometric principles to the
characteristic spectral correlations of the quantum ergodic phase.
