String theory (!) and "bad metals"

I saw a remarkable talk today by Hong Liu from MIT, about quantum gravity and what it has to say about high temperature superconductivity.  Yes, you read that correctly.  It was (at least for a nonexpert) a reasonably accessible look at a genuinely useful physics result to come from string theory.  I doubt I can do it justice, so I'll just give the bare-bones idea.  Within string theory, Maldacena (and others following) showed that there is a duality (that is, a precise mathematical correspondence) between some [quantum theories of gravity in some volume of d+1 dimensions] and some [quantum field theories w/o gravity on the d-dimensional boundary of that volume].  This sounds esoteric - what could it be good for?  Well, we know what we think the classical limit of quantum gravity should be:  Einstein's general relativity, and we know a decent number of solutions to the Einstein equations.  The duality means that it is possible to take what could be a very painful interacting many-body quantum mechanics problem (say, the quantum field theory approach to dealing with a large number of interacting electrons), and instead of solving it directly, we could convert it into a (mathematically equivalent) general relativity problem that might be much simpler with a known solution.  People have already used this approach to make predictions about the strongly-interacting quark-gluon plasma produced at RHIC, for example.


I'd known about this basic idea, but I always assumed that it would be of very limited utility in general.  After all, there are a whole lot of possible hard many-body problems in solid state physics, and it seemed like we'd have to be very lucky for the duals of those problems to turn out to be easy to find or solve.  Well, perhaps I was wrong.  Prof. Liu showed an example (or at least the results), in which a particular general relativity solution (an extremal charged blackhole) turns out to give deep insights into a long-standing issue in the strongly-correlated electron community.  Some conducting materials are said to be "bad metals".  While they conduct electricity moderately well, and their conductivity improves as temperature goes down (one definition of metal), the way that the conductivity improves is weird.  Copper, a good metal, has an electrical resistance that scales like T² at low temperatures.  This is well understood, and is a consequence of the fact that the low-energy excitations of the electrons in copper act basically like noninteracting electrons.  A bad metal, in contrast, has a resistance that scales like T, which implies that the low energy excitations in the bad metal are very complex, rather than electron-like.  Well, looking at the dual to the extremal black hole problem actually seems to explain the properties of this funny metallic state.  A version of Prof. Liu's talk is online at the KITP.  Wild stuff!  It's amazing to me that we're so fortunate that this particular correspondence exists.