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AdS/CFT: a working hologram (in the math)
1997· Theory
Well supportedStrong evidence or math, but not fully tested.
Maldacena's 1997 conjecture, now heavily checked, that a universe with gravity can be exactly equivalent to a gravity-free quantum theory living on its boundary.
See it on the Science map →How it works
AdS is anti-de Sitter space: a saddle-curved universe with an edge. CFT is a conformal field theory: a quantum theory of particles, like a cousin of the strong force, with no gravity. The claim is a perfect translation: every event inside the 5D curved space, including black holes, matches some event in the 4D boundary theory. Hard problems on one side can become easy on the other, so physicists use it as a calculator.
Why it matters
It is the clearest working example of holography, and strong evidence that black holes do not destroy information, since the boundary theory never loses any.
Think of it like
Like two complete sets of books for the same company, one by cash and one by accrual: they look nothing alike, yet every transaction appears in both.
How we know
Thousands of mathematical checks match quantities computed on both sides. It predicted the quark-gluon plasma at Brookhaven's RHIC flows with almost no friction, roughly as measured around 2005. Not rigorously proven.
Still a mystery
Our universe is expanding with positive dark energy, the opposite of anti-de Sitter. Whether a similar dictionary exists for our universe is a major open problem.
Connections (4)
▸String theory led to AdS/CFT: a working hologram (in the math)Well supported
The relationship
String theory contains membranes called D-branes. Maldacena studied a stack of them two ways: as particles moving on the branes, with no gravity, and as strings bending space around the branes, with gravity. Since both describe one system, he concluded the gravity theory and the gravity-free particle theory must be equivalent: AdS/CFT.
How the link was found
Joseph Polchinski identified D-branes in 1995. Juan Maldacena made the leap in late 1997. Steven Gubser, Igor Klebanov, Alexander Polyakov and Edward Witten supplied the translation rules in 1998.
Is it proven?
Thousands of calculations agree on both sides, including symmetry matches and black-hole entropy counts. Within string theory the evidence is strong, though no complete mathematical proof exists.
Open questions and mysteries
Whether the duality needs string theory at all, or is a broader fact about gravity, is open.
▸The holographic principle is made precise in AdS/CFT: a working hologram (in the math)Well supported
The relationship
The holographic principle was a general suspicion: a region's contents are encoded on its boundary. AdS/CFT is a fully specified example. Everything inside a 5D anti-de Sitter universe, gravity and black holes included, is exactly reproduced by a 4D quantum theory on its edge, with explicit rules for translating between the two.
How the link was found
Juan Maldacena (1997) gave the example. Edward Witten's 1998 paper "Anti de Sitter space and holography" explicitly linked it to 't Hooft and Susskind's principle.
Is it proven?
Boundary calculations reproduce black-hole entropy and other interior quantities. In 2006 Shinsei Ryu and Tadashi Takayanagi showed boundary entanglement equals interior surface areas, a sharp holographic match.
Open questions and mysteries
Our universe is not anti-de Sitter. Proposals for holography of expanding universes, such as dS/CFT (2001), are incomplete.
▸Juan Maldacena discovered AdS/CFT: a working hologram (in the math)Well supported
The relationship
Maldacena compared two descriptions of the same stack of string-theory membranes and noticed that, at low energies, one became a pure particle theory and the other became gravity in curved space. He boldly conjectured they were the same theory in different clothes, and laid out how quantities on each side match.
How the link was found
Juan Maldacena, posted November 1997 and published 1998, while at Harvard. It became among the most cited papers in high-energy physics.
Is it proven?
Thousands of follow-up checks agree. He received the 2012 Breakthrough Prize partly for it. It remains a conjecture without full mathematical proof.
Open questions and mysteries
Why the duality works so well, and whether a deeper principle underlies it, is still being explored.
▸AdS/CFT: a working hologram (in the math) shows how space can arise, supporting Space and time may be emergentWell supported
The relationship
In AdS/CFT the boundary theory has one fewer dimension than the interior. The extra dimension is not built in; it arises from how the boundary particles are organized and entangled. That is a working demonstration that space can be an output, not an input, which supports the broader idea that our space emerges too.
How the link was found
Maldacena (1997) gave the framework. Shinsei Ryu and Tadashi Takayanagi (2006) linked interior areas to entanglement, and Mark Van Raamsdonk (2010) argued space is built from entanglement.
Is it proven?
Within the models the math is solid and widely checked. It has not been shown for our universe.
Open questions and mysteries
Time is not emergent in AdS/CFT; the boundary already has it. Whether time can emerge as space does is unknown.