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

TL;DR

This paper develops methods to compute the bulk-to-boundary propagator in black hole microstate backgrounds within AdS$_3$/CFT$_2$, revealing discrepancies with semiclassical theory and providing insights into quantum gravitational effects.

Contribution

It introduces a novel approach to calculate the bulk-to-boundary propagator in black hole microstates at finite central charge, advancing understanding of quantum gravity in AdS$_3$ backgrounds.

Findings

Exact reconstruction of propagators using CFT$_2$ data and Virasoro symmetry.

Discrepancy between semiclassical Euclidean BTZ and exact quantum descriptions.

Potential exponential suppression of quantum effects for physical observers.

Abstract

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, $\langle \phi_L \mathcal{O}_L \mathcal{O}_H \mathcal{O}_H\rangle$, 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.