Wormholes and surface defects in rational ensemble holography

We study wormhole contributions to the bulk path integral in holographic models which are dual to ensembles of rational free boson conformal field theories. We focus on the path integral on a geometry connecting two toroidal boundaries, which should capture the variance of the ensemble distribution. We show that this requirement leads to a nontrivial set of constraints which generically picks out the uniform, maximum entropy, ensemble distribution. Furthermore, we show that the two-boundary path integral should receive contributions from ‘exotic’ wormholes, which arise from the inclusion of topological surface defects.