A numerical approach to Virasoro blocks and the information paradox

Abstract

Abstract We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit correspond-ing to a light probe propagating in a BTZ black hole background. In the Lorentzian regime, we find empirically that the initial exponential time-dependence of the blocks transitions to a universal t − 3 2 $$ t-\frac{3}{2} $$ power-law decay. For the vacuum block the transition occurs at t ≈ π c 6 h L $$ t\approx \frac{\uppi c}{6{h}_L} $$ , confirming analytic predictions. In the Euclidean regime, due to Stokes phenomena the naive semiclassical approximation fails completely in a finite region enclosing the ‘forbidden singularities’. We emphasize that limitations on the reconstruction of a local bulk should ultimately stem from distinctions between semiclassical and exact correlators.

Keywords

• 1/N Expansion
• AdS-CFT Correspondence
• Black Holes
• Conformal and W Symmetry