Tuesday, September 23, 2008

Nonrelativistic AdS/cold atoms correspondence

We have talked about the application of string-theoretical methods in heavy ion physics and condensed matter physics.

Recently, several people became interested in another discipline that could be overrun by string theory ;-), namely atomic physics.

Free fermions as well as the so-called fermions at unitarity might have dual AdS-like gravitational descriptions - that would only differ by boundary conditions - even though the details are not known.

However, a sensible candidate geometry is known and it has the desired symmetry, namely the Schrödinger symmetry, a nonrelativistic subgroup of the conformal symmetry which is the symmetry of the Schrödinger equation. It includes the Galileo group, scaling of time and space by different power laws, and some special conformal transformations.

As I said, the precise hypothetical dual theory is not known (for example, the replacement for the "number of colors" seems unclear) which is why I don't view the proposal too seriously at this moment but the relevant bulk geometry has two additional dimensions, rather than one that we are used to from holography. The other one is a compact light-like direction. And a few additional consistency checks work, too.

Shamit Kachru: a popular review
Jester at Resonaances: a popular review
Balasubramanian & McGreevy: a technical paper
D.T. Son: a technical paper

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