Virasoro Blocks and the Black Hole Information Paradox

Abstract

This thesis explores the black hole information paradox within the context of AdS3/CFT2, focusing on BTZ black holes and the role of Virasoro conformal blocks in encoding quantum gravitational effects. The main object of study is the four-point CFT correlator, which manifests key signatures of information loss: the presence of “forbidden singularities” in Euclidean correlators and the late-time exponential decay of Lorentzian correlators. These effects signal a breakdown of the semi-classical approximation, and suggest the presence of non-perturbative corrections in unitarity and information restoration. To understand these corrections, this thesis investigates the structure of Virasoro conformal blocks, particularly in the large central charge c limit. The vacuum block, in particular, serves as a universal probe of information loss, encoding the effects of multigraviton exchanges between probe scalars in AdS3. We review work done on degenerate Virasoro blocks and their analytic continuation to understand semi-classical Virasoro blocks in the heavy-light limit and investigate the so-called Master Equation that includes non-perturbative finite c effects. Different scaling regimes near the forbidden singularities are tested and verified to match with perturbative 1/c corrections to the block, which are known via field-theoretic methods previously. The thesis further explores the connection between Virasoro blocks and geodesic Witten diagrams, which provide a holographic prescription for computing these blocks in the bulk. A novel prescription for constructing the bulk dual of Virasoro blocks specifically for the case of BTZ black holes is proposed. We hope that this refines the existing approaches and offers insights into how the bulk-bulk propagator (AdS Green’s function) is intimately connected to Virasoro blocks. By reviewing non-perturbative corrections and finding novel bulk interpretations, this thesis extends the understanding of the black hole information paradox in AdS3/CFT2, providing new perspectives on unitarity restoration and the role of the black hole horizon in quantum gravity.