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In physics, the AdS/CFT correspondence (anti de Sitter/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory and gravity defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more. The name suggests that the first space is the product of anti de Sitter space (AdS) with some closed manifold like sphere, orbifold, or noncommutative space, and that the quantum field theory is a conformal field theory (CFT).[1]

http://en.wikipedia.org/wiki/AdS/CFT_correspondence

              Synopsis: Gravity Finds a New Partner APS

Gravity dual of the Ising model

Alejandra Castro, Matthias R. Gaberdiel, Thomas Hartman, Alexander Maloney, and Roberto Volpato

Phys. Rev. D 85, 024032 (2012)
Published January 19, 2012
The classical description of gravity fails when looking at interactions at small length scales, but developing a quantum theory for gravity has proven to be one of the most fundamental challenges in physics. For such a theory to be realistic, it needs to describe gravity in four dimensions—three spatial dimensions, plus time. But theorists can learn from simpler, three-dimensional (3D) theories. And, some of these 3D theories for gravity (those in a so-called anti-de Sitter space) can be mapped to two-dimensional conformal field theories, which can be solved. These 2D field theories are said to live at the boundary of spacetime described by the 3D theory for gravity.

Now, in a theoretical paper appearing in Physical Review D, Alejandra Castro of McGill University, Canada, and her colleagues argue that one of these dual conformal field theories is the critical Ising model in two dimensions, a well-understood model for describing magnetic phase transitions in a lattice of interacting spins. The gravity theory involved in this duality is strongly coupled, meaning quantum effects are important.



There are many exactly solvable conformal field theories
(CFTs) in two dimensions, some of which describe
important statistical systems. According to the AdS/CFT
correspondence such theories are expected to be dual to
theories of quantum gravity in three dimensions. Given the
simplicity of the boundary theory, these dualities, if fully
understood, would likely shed light on the nature of holography
and the emergence of geometry from quantum
field theory. Potential examples have been studied in the
semiclassical regime (see e.g. [1–3]) but so far there is no
completely satisfactory example of a fully quantum theory
of gravity which is dual to an exactly solvable 2d CFT.
In this paper we will argue that a class of exactly
solvable CFTs are dual to certain theories of quantum
gravity in AdS3. These are strongly coupled gravity theories
where the AdS radius is Planck scale. Nevertheless, the
path integral of quantum gravity can—with certain assumptions—
be computed exactly and agrees with that of
a known minimal model CFT. The simplest example is the
Ising model, which we conjecture to be dual to Einstein
gravity with a particular (Planck scale) value of the cosmological
constant.

http://physics.aps.org/synopsis-for/10.1103/PhysRevD.85.024032


This requires the past and future horizons to be dS/CFT dual (dark energy) at least for the future horizon. Maybe the past horizon is AdS/CFT dual (dark matter).


Tamara Davis Ph.D. Fig 1.1c
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