Mathematics

How to get a superconductor out of a black hole
Chris. P. Herzog, Princeton University

Gauge/gravity duality, a concept which emerged from string theory, holds promise for revealing the secrets of certain strongly interacting real world condensed matter systems. Historically, string theorists presented their subject as a promising framework for a quantum theory of gravity. More recently, the AdS/CFT correspondence and gauge/gravity dualities have emerged as powerful tools for using what we already know about gravity to investigate the properties of strongly interacting field theories. I will cherry pick and discuss a few recent developments where black holes are used to calculate the thermodynamic and transport properties of quantum critical systems, superconductors, and superfluids.

For strongly interacting systems, calculating transport properties such as charge conductivities and diffusion constants has historically been a difficult enterprise. Standard techniques, such as perturbation theory and lattice gauge theory, are not trustworthy, perturbation theory because it assumes the interactions are weak and lattice gauge theory because numerical techniques often fail when confronted with time dependence and non-zero densities.

In contrast, gauge/gravity dualities provide a simple and easy method to calculate transport coefficients. The challenge when employing these dualities is to find a gravitational model that is dual to a system of real world physical importance. Thus far, we have been able to construct dual pairs with tantalizing similarities to real world systems, pairs for example which undergo superfluid or superconducting phase transitions. A next step is to use these dualities to make quantitative predictions about the real world.

See my lecture notes, arxiv.org/abs/0904.1975, for a more detailed discussion.

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Mathematics

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