Condensed matter applications of the Gauge/Gravity correspondence

Abstract

In this thesis, we investigate non-perturbative features of strongly coupled condensed matter systems, generically, placed at finite temperature, charge density and, possibly, in a magnetic field using the theoretical framework of the gauge/gravity correspondence. According to the dictionary of the duality, such field theories are related to charged black holes in one dimension higher that emerge from weakly interacting gravity theories. Following this approach, progress has been made in understanding some of the universal features of field theories at strong coupling, with new classes of black holes being discovered along the way.

The bulk of the thesis consists of four interconnected parts. In the first, we study magnetically charged black holes and we find that, at some critical temperature, a new branch of spatially modulated branes appears, corresponding to a dual field theory with a current density wave. In the second part, we investigate the ground state of strongly coupled field theories placed in magnetic field, within the context of gauged supergravity in D=4,5 dimensions. This analysis revealed a rich structure of instabilities and, in particular, showed that only the supersymmetric solutions correspond to stable configurations. In the third part, we consider a generalised version of local quantum critical points, called η-geometries, in the context of U(1)^4 supergravity in D=4 dimensions. We show that the latter theory admits extremal black holes carrying three non-zero electric or magnetic charges which approach an η=1 geometry in the IR, while a small fourth charge resolves the singularity of the η-geometry replacing it with an AdS_2XR^2 factor in the far IR. Finally, in the last part, we discuss the possibility of spatially modulated superconductors. We construct electrically charged black holes dual to four dimensional CFTs in a superfluid phase with either p-wave or (p+ip)-wave order and we discuss their thermodynamic properties, the corresponding ground states as well as the competition of the two types of order.