The Bulk-to-Boundary Propagator in Black Hole Microstate Backgrounds

First-quantized propagation in quantum gravitational AdS${}_3$ backgrounds can be exactly reconstructed using CFT${}_2$ data and Virasoro symmetry. We develop methods to compute the bulk-to-boundary propagator in a black hole microstate, $⟨{\varphi }_L{\mathcal{O}}_L{\mathcal{O}}_H{\mathcal{O}}_H⟩$, at finite central charge. As a first application, we show that the semiclassical theory on the Euclidean BTZ solution sharply disagrees with the exact description, as expected based on the resolution of forbidden thermal singularities, though this effect may appear exponentially small for physical observers.