Abstract:

Classically, the volume of the Einstein-Rosen bridge of the two-sided black hole grows linearly in time. Such linear increase is in conflict with the finite black hole entropy S, thus at late time, the volume should be upper-bounded and saturate at the time scale O(e^S). The bulk mechanism of such saturation is due to the production of baby universes which shorten the ER bridge. In this talk, we construct a family of codimension-zero observables non-perturbatively that probe the quantum properties of the ER bridge at late time. This construction allows us, for example, to study the late-time behavior of the Wheeler-de-Witte action which is conjectured to be dual to the state complexity. The new important element in the codimension-zero observables is the presence of “operator wormholes,” which are the baby universes emanating from the codimension-zero region. We find that along with the bra-ket wormholes that shorten the ER bridge, these operator wormholes have a significant impact on the late-time behavior of the codimension-zero observables.