AdS-CFT correspondence and the information paradox

Abstract

The information paradox in the quantum evolution of black holes is studied within the framework of the AdS/CFT correspondence. The unitarity of the CFT strongly suggests that all information about an initial state that forms a black hole is returned in the Hawking radiation. The CFT dynamics implies an information retention time of order the black hole lifetime. This fact determines many qualitative properties of the non-local effects that must show up in a semi-classical effective theory in the bulk. We argue that no violations of causality are apparent to local observers, but the semi-classical theory in the bulk duplicates degrees of freedom inside and outside the event horizon. Non-local quantum effects are required to eliminate this redundancy. This leads to a breakdown of the usual classical-quantum correspondence principle in Lorentzian black hole spacetimes.March, 1999

Local bulk operators in AdS/CFT correspondence: A boundary view of horizons and locality

“…Our construction is applicable in the limit of semiclassical supergravity; it would be extremely interesting to understand 1/N and α ′ corrections. Non-local operators in the CFT should provide a new tool to study bulk phenomena such as black hole singularities [23,24], the interplay of holography and locality [25], or even non-local deformations of AdS [26]. But at a more fundamental level, one might ask: purely from the boundary CFT point of view, what if anything would allow one to identify a particular set of non-local operators as appropriate for describing bulk spacetime?…”

“…It is simplest to work in terms of a mode sum in frequency space. From (17) or (25) one sees that the smearing is done by multiplying each mode of the boundary operator by a frequency dependent phase. These phases act as a regulator which makes the correlator with most other operators non-singular.…”

“…The Poincaré smearing function in frequency space can be read off from (25), It is important to note that, even in the center of AdS, the lightcone singularities of the bulk theory arise from the UV behavior of the boundary theory. This means, for example, that any attempt to put a UV cutoff on the boundary theory will modify locality everywhere in the bulk.…”

Quasiparticle picture of black holes and the entropy-area relation

“…It is closely related to the membrane paradigm description of black holes [15]. It also has significant overlap with the work of Susskind and others on black hole complementarity [16,17,18,19,20,21,22]. …”

Black hole complementarity and firewall in two dimensions

“…In particular, the efforts to resolve the information loss problem appear in the form of so called black hole complementarity [2]. The principle of black hole complementarity is closely related to the membrane paradigm [3], the D-brane picture [4], and the AdS/CFT correspondence [5].…”