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 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 − 3 2 power-law decay. For the vacuum block the transition occurs at t ≈ πc 6h 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.

An exact operator that knows its location

“…Many aspects of black hole thermodynamics are encoded in the Virasoro algebra at large central charge [49][50][51][52][53], including various non-perturbative effects that resolve or ameliorate information loss problems [54][55][56]. This means that it should be possible to learn about bulk physics in the presence of black holes using Virasoro technology.…”

“…Furthermore, general considerations [57] borne out by non-perturbative investigations of Virasoro blocks [56] show that in Euclidean space, pure high-energy quantum states look very different from the BTZ black hole solution in the vicinity of the horizon. This follows from the fact that thermal and BTZ correlators are periodic in Euclidean time, while pure state correlators display completely unsuppressed violations of this periodicity [56].…”

“…This follows from the fact that thermal and BTZ correlators are periodic in Euclidean time, while pure state correlators display completely unsuppressed violations of this periodicity [56]. Thus we have reason to believe that correlators like φφO H O H will tell us about interesting structures near the Euclidean horizon.…”

2D CFT partition functions at late times

“…3 See [19] for recent developments. 4 The torus partition function can be written as a correlator involving 4 heavy twist operators.…”

“…Strictly speaking, the manipulations we present are only valid for w > 1, but we may think of introducing w as a regulator. 19 The final results can be analytically continued to w = 0. They match careful computations performed in the w < 1 regime with a subtraction based scheme [38,39].…”