Holographic description of a quantum black hole on a computer

Abstract

The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of quantum mechanics may be violated. A possible cure appeared recently from superstring theory, a consistent theory of quantum gravity: if the holographic description of a quantum black hole based on the gauge/gravity duality is correct, the information is not lost and quantum mechanics remains valid. Here we test this gauge/gravity duality on a computer at the level of quantum gravity for the first time. The black hole mass obtained by Monte Carlo simulation of the dual gauge theory reproduces precisely the quantum gravity effects in an evaporating black hole. This result opens up totally new perspectives towards quantum gravity since one can simulate quantum black holes through dual gauge theories.

The BFSS model on the lattice

“…The dashed curve at low temperature represents the prediction of gauge/gravity. 13 The model becomes unstable for small matrix sizes N , an effect which has been related to Hawking radiation in the dual gravitational theory [30,32]. To compare with the gauge/gravity predictions one needs to consider large matrices.…”

Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N

“…Our use of T is precisely related to the fact that we are assuming a non-trivial scaling dynamics at low temperatures, and indeed for temperatures well below the scale ∼ 1/L, and therefore it should be this lowest scale that determines the behaviour of quantities such as derivatives. 14 We obtain our usual black Dp-brane behaviour if we treat the correction term as negligible. However, we must check to ensure this assumption is self consistent, which requires that L |φ ab | 1 in the expression above in order to suppress the correction term.…”

“…One promising analytic approach, explored for p = 0 is a method analogous to the mean field approximation [5][6][7], although recent work indicates that one still cannot see the above thermal behaviour [8]. Numerical approaches were initiated for p = 0 in [9][10][11][12] and confirmed the behaviour predicted by gravity, with the latest results being [13,14]. For p = 1 numerical evidence [15] also supports predictions from gravity.…”

“…More precisely, the energy density of the SYM integrated over the compact circle should give the energy density of a non-compact black D(p − 1)-brane solution. So for L L c we expect 2πL 0 dx p to be given by equation (2.36) with 14 If we had taken anti-periodic boundary conditions on a spatial circle, then we would not obtain such a non-trivial dynamics at low temperature, and this would be reflected by estimating ∂ ∼ π max 1 β , 1 2πL , and a transition in behaviour will occur at 2πL = β where the lowest scale is flipped. A corresponding phase transition does indeed occur in the dual supergravity [55][56][57].…”

Towards a finite-N hologram

“…To the best of our knowledge however, there is no known example where a holographic theory is fully solvable exactly for arbitrary tunable values of N . This is not just a matter of being pedantic, there are strong reasons [12][13][14][15][16][17][18] to think that unitarization of black holes (for example), will require 1 one to understand non-perturbative corrections in 1/N .…”