# A Numerical Approach to Virasoro Blocks and the Information Paradox

## TL;DR

This paper numerically analyzes Virasoro conformal blocks in a heavy-light limit to understand the breakdown of semiclassical gravity and the information paradox, revealing universal decay behaviors and limitations of semiclassical approximations.

## Contribution

It provides high-precision numerical analysis of Virasoro blocks, demonstrating the transition from exponential to power-law decay and elucidating the failure of semiclassical approximations near forbidden singularities.

## Key findings

- Exponential decay transitions to t^{-3/2} power-law decay.
- Transition time matches analytic predictions.
- Naive semiclassical approximation fails near forbidden singularities.

## Abstract

We chart the breakdown of semiclassical gravity by analyzing the Virasoro conformal blocks to high numerical precision, focusing on the heavy-light limit corresponding 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 $t^{-\frac{3}{2}}$ power-law decay. For the vacuum block the transition occurs at $t \approx \frac{\pi c}{6 h_L}$, 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.