A popular trend in modern fundamental physics is to reconsider various, sometimes very well known,
phenomena from the point of view of holography. Holography is a rather general statement that the
physics inside a spatial region can be understood by looking at a certain theory defined on the
boundary of the region. This holographic principle was first formulated by ’t Hooft [215] and later
generalized by Susskind [212]. For a review of the holographic principle see [24]. A concrete
realization of holography is the AdS/CFT correspondence [167, 223, 125]. According to this
correspondence the theory of supegravity (more precisely string theory, the low energy regime of
which is described by supegravity) in a
-dimensional anti-de Sitter spacetime (AdS) is
equivalent to a quantum conformal field theory (CFT) defined on a
-dimensional boundary of
the anti-de Sitter. There is a precise dictionary definition of how phenomena on one side of
the correspondence can be translated into phenomena on the other side. The correspondence
has proven to be extremely useful, both for better understanding gravitational physics and
quantum field theory. If
, then the CFT on the boundary is known to be an
superconformal gauge theory. This theory is strongly coupled and in many aspects resembles
the QCD. Thus utilizing the correspondence one, in particular, may gain some information
on how theories of this type behave (for a review on the correspondence and its applications
see [1]).
One of the aspects of the AdS/CFT correspondence is geometrical. The boundary theory provides
certain boundary conditions for the gravitational theory in bulk so that one may decode the
hologram: reconstruct the bulk spacetime from the boundary data. As was analyzed in [60], for this
reconstruction, the boundary data one has to specify consist of the boundary metric and the vacuum
expectation of the stress-energy tensor of the boundary CFT. The details are presented in [60
]; see
also [193].
Entanglement entropy is one of the fundamental quantities, which characterize the boundary theory.
One would think that it should have an interpretation within the AdS/CFT correspondence. This
interpretation was suggested in 2006 by Ryu and Takayanagi [189, 188
] (for a review on this proposal
see [185]). This proposal is very interesting since it allows one to compute the entanglement entropy in a
purely geometrical way (see also [109]).
http://www.livingreviews.org/lrr-2011-8 |
Living Rev. Relativity 14, (2011), 8
![]() This work is licensed under a Creative Commons License. E-mail us: |