A Numerical Approach to Virasoro Blocks and the Information Paradox

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.Comment: 45 pages, 23 figure

Numerical Computations in Conformal Field Theory

This thesis discusses two major computational projects in conformal field theory (CFT) and the interpretation of their results. The first, concerning the Virasoro Conformal Blocks of 2-dimensional CFT, uses dynamic programming and extreme precision arithmetic to prove that information is not lost after it falls into a black hole in 3-dimensional anti-de Sitter spacetime. The second, a 3-dimensional realization of a generic CFT technique called conformal truncation, uses a truncated basis of operators to naturally map CFT questions to finite-dimensional linear algebra problems, then solves them with dynamic programming and large matrix methods. To demonstrate the correctness of the program, we use it to show the closure of the mass gap in the 3D Ising model