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 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 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.

We present a field theory description for the non-perturbative splitting and joining of baby universes in Euclidean Jackiw-Teitelboim (JT) gravity. We show how the gravitational path integral, defined as a sum over topologies, can be reproduced from the perturbative expansion of a Kodaira-Spencer (KS) field theory for the complex structure deformations of the spectral curve. We use that the Schwinger-Dyson equations for the KS theory can be mapped to the topological recursion relations. We refer to this dual description of JT gravity as a ‘universe field theory’. By introducing non-compact D-branes in the target space geometry, we can probe non-perturbative aspects of JT gravity. The relevant operators are obtained through a modification of the JT path integral with Neumann boundary conditions. The KS/JT identification suggests that the ensemble average for JT gravity can be understood in terms of a more standard open/closed duality in topological string theory.

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)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 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.