The $α$-states of a string worldsheet

The worldsheet description of string amplitudes can be reinterpreted as a baby universe field theory. Under this reinterpretation, we determine the $\alpha$-states of a topological string theory: the Hurwitz worldsheet. We find that their relation to the Hartle--Hawking state encodes foundational results in the asymptotic representation theory of the symmetric group. In the holographic dual, our results characterize the pseudorandom nature of an ensemble of cluster-decomposing correlators.