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AdS-CFT in condensed matter physics

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Context

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

under construction

Contents

Idea

The AdS-CFT correspondence applies exactly only to a few highly symmetric quantum field theories, notably to N=4 D=4 super Yang-Mills theory. However, it does not completely break away from these special points in field theory space, but applies in some approximation and/or with suitable modifications on the gravity-side of the correspondence.

For instance quantum chromodynamics (one sector of the standard model of particle physics) is crucially different from but still similar enough to N=4 D=4 super Yang-Mills theory that some of its observables, in particular otherwise intractable non-perturbative effects, have been argued to be usefully approximated by AdS-CFT-type dual gravity-observables, for instance the shear viscosity of the quark-gluon plasma. This is hence also called the AdS/QCD correspondence.

Similarly, as far as systems in condensed matter physics are described well by some effective field theory, one may ask whether this, in turn, is usefully related to gravity on some anti de-Sitter spacetime? and use this to study the solid state system, notably its non-perturbative effects.

Andreas Karch writes here:

These anomalous transport coefficients have first been calculated in AdS/CFT. The relevant references are [8], [9] and [10] in the Son/Surowka paper. In the AdS/CFT calculations these particular transport coefficients only arise due to Chern-Simons terms, which are the bulk manifestation of the field theory anomalies. At that point it was obvious to many of us that there should be a purely field theory based calculation, only using anomalies, that can derive these terms. Son and Surowka knew about this. They were sitting next door to me when they started these calculations. Many of us tried to find these purely field theory based arguments and failed. Son and Surowka succeeded.

If you ask anyone serious about applying AdS/CFT to strongly coupled field theories why they are doing this, they would (hopefully) give you an answer along the lines of “AdS/CFT provides us with toy models of strongly coupled dynamics. While the field theories that have classical AdS duals are rather special, we can still learn important qualitative insights and find new ways to think about strongly coupled field theories.” Once AdS/CFT stumbles on a new phenomenon in these solvable toy models, we want to go back to see whether we can understand it without the crutch of having to rely on AdS/CFT. Any result that only applies in theories with holographic dual is somewhat limited in its applications. In this sense, anomalous transport is a poster child for what AdS/CFT can be used for: a new phenomenon that had been missed completely by people studying field theory gets uncovered by studying these toy models. Once we knew what to look for, a purely field theoretic argument was found that made the AdS/CFT derivation obsolete.

This is applied AdS/CFT as it should be. Solvable examples exhibit new connections which then can be proven to be correct more generally and are not limited to the toy models that were used to uncover them.

References

A comprehensive textbook account is in

Reviews include the following:

Last revised on July 3, 2019 at 11:57:36. See the history of this page for a list of all contributions to it.