The Page curve of Hawking radiation from semiclassical geometry

Two-dimensional Yang-Mills theory is a useful model of an exactly solvable gauge theory with a string theory dual at large N . We calculate entanglement entropy in the 1/N expansion by mapping the theory to a system of N fermions interacting via a repulsive entropic force. The entropy is a sum of two terms: the "Boltzmann entropy", log dim(R) per point of the entangling surface, which counts the number of distinct microstates, and the "Shannon entropy", − p R log p R , which captures fluctuations of the macroscopic state. We find that the entropy scales as N 2 in the large N limit, and that at this order only the Boltzmann entropy contributes. We further show that the Shannon entropy scales linearly with N , and confirm this behaviour with numerical simulations. While the term of order N is surprising from the point of view of the string dual -in which only even powers of N appear in the partition function -we trace it to a breakdown of large N counting caused by the replica trick. This mechanism could lead to corrections to holographic entanglement entropy larger than expected from semiclassical field theory.

Section: Discussionmentioning

confidence: 99%

Entanglement entropy and the large N expansion of two-dimensional Yang-Mills theory

Donnelly

Timmerman

Valdés-Meller

2020

“…Below we analyze a CFT 2 joining quench, over which we have complete field theory (and holographic) control. A complication arises: the joining creates a shock of energy as in [29,30], which propagates through the system ballistically. While the time evolution of the entropy is identical to that in (33), the membrane theory description seems to be a lot more complicated in this case, as we explain in detail.…”

Section: A Simple Holographic Modelmentioning

confidence: 99%

Exploring the membrane theory of entanglement dynamics

Virrueta

2020

Recently an effective membrane theory valid in a "hydrodynamic limit" was proposed to describe entanglement dynamics of chaotic systems based on results in random quantum circuits and holographic gauge theories. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to hydrodynamics, joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to higher derivative gravity and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.

“…For this simple two-dimensional model, the backreaction can be explicitly calculated because of the topological nature of JT gravity. 3 Additionally, the von Neumann entropy of CFT 2 , defined by the analog of Shannon entropy for quantum states ρ, S bulk (ρ) = −Trρ log ρ (1.1)…”

Section: Introductionmentioning

confidence: 99%

Information flow in black hole evaporation

Chen

Fisher

Hernandez

et al. 2020

151

Recently, new holographic models of black hole evaporation have given fresh insights into the information paradox [1][2][3]. In these models, the black hole evaporates into an auxiliary bath space after a quantum quench, wherein the holographic theory and the bath are joined. One particularly exciting development is the appearance of 'ER=EPR'-like wormholes in the (doubly) holographic model of [3]. At late times, the entanglement wedge of the bath includes the interior of the black hole. In this paper, we employ both numerical and analytic methods to study how information about the black hole interior is encoded in the Hawking radiation. In particular, we systematically excise intervals from the bath from the system and study the corresponding Page transition. Repeating this process ad infinitum, we end up with a fractal structure on which the black hole interior is encoded, implementing theüberholography protocol of [4].