Jan Zaanen

Perhaps the most fundamental mystery in quantum matter is the general nature of matter formed from fermions, like the electrons. The methods of many body quantum physics fail because of the fermion sign problem and one can only rely on the phenomenological Fermi-liquid theory and its BCS-type derivatives. This has a direct bearing on the problem of high Tc superconductivity: surely in heavy fermion systems, but likely also in the optimally doped cuprates, the metallic state is a quantum critical state formed from fermions, and to understand the superconducting transition one needs to understand the normal state first. Remarkably, it might well be that the mathematics developed by string theorists is capable of describing such states of fermion matter. The so-called AdS/CFT correspondence translates the problem of strongly interacting (near) critical quantum matter into an equivalent general-relativity problem involving the propagation of classical fields in an Anti-de-Sitter space-time with a black hole in its center. This development of string theory meeting reality started some time ago with the demonstration that AdS/CFT predicts correctly the low viscosity of the near quantum critical quantum-gluon plasma as created at the Brookhaven heavy ion collider. Very recently the focus has shifted to the way AdS/CFT processes fermions, creating much excitement: it appears that both emergent heavy Fermi-liquids as well as non Fermi-liquids having a ‘marginal’ attitude can be encoded, going hand in hand with ‘holographic’ superconductors having suggestive traits in common with the real life high Tc variety.