Nature has an article about a nifty and relatively new application of ideas born out of string theory: to understand what happens in high-temperature superconductors! The story goes something like this.

Take a sample of some material which can conduct electricity, and apply two kinds of outside influence upon it. First, stick it in a magnetic field pointing in some direction, and second, apply a temperature gradient in a direction perpendicular to the magnetic field. In some substances, an electric field will appear, perpendicular to both the magnetic field and the temperature gradient. This is called the Nernst effect. It doesn’t happen very much with ordinary metals, but in semiconductors — like silicon or germanium — it can be quite noticeable. It also appears in some superconductors, like Y-Ba-Cu-O and CeCoIn₅ to name but two.

Sean A. Hartnoll et al. have cooked up a theory to explain the Nernst effect and other behaviors seen in the cuprate superconductors, ceramic compounds containing copper. Looking at the situation near the phase transition, where a substance is “on the verge” of changing from insulator to superconductor, they developed a theory involving the magnetic field, call it [tex]B[/tex], and fluctuations in the material’s density, [tex]\rho[/tex]. Then they looked at this theory in the conceptual mirror known as the AdS/CFT correspondence. This connection between seemingly disparate ideas takes you from a “conformal field theory,” the sort of math involved with the superconductor problem (among other things), to a theory of gravity in a type of universe called anti-de Sitter space. In this mirror-world description, the perturbations in [tex]B[/tex] and [tex]\rho[/tex] become magnetic and electric charges of a black hole sitting in the AdS universe!

This chicanery becomes useful because easy problems in one description often correspond to hard problems in the other. Thus, you can study the black hole and learn about its counterpart, even when the counterpart is too complicated to approach directly.

Hartnoll and company were able to extract details on how their superconductor model behaves by looking at its black-hole dual. In their words,

This is the power of the AdS/CFT correspondence: all transport phenomena of the strongly correlated CFT at large N are reduced to solving the equations for classical perturbations of the dual black hole in Einstein-Maxwell theory.

(Via Peter Steinberg at Entropy Bound.)

SEE:

• Hartnoll, S.A., Kovtun, P.K., Müller, M., Sachdev, S. (2007). Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes. Physical Review B, 76(14) DOI: 10.1103/PhysRevB.76.144502; arXiv:0706.3215.