Applications of holography to condensed matter physics

Abstract

Holography is one of the key insights to emerge from string theory.It connects quantum gravity to field theory, and thereby provides anon-perturbative formulation of string theory. This has enabledprogress on a range of theoretical issues, from the quantumdescription of spacetime to the calculation of scattering amplitudesin supersymmetric field theories. There have been important insightsinto both the field theories and the spacetime picture.More recently, applied holography has been the subject of intense andrapid development. The idea here is to use the spacetime descriptionto address questions about strongly coupled field theory relevant toapplication areas such as finite-temperature QCD and condensed matterphysics; the focus in this special issue is on the latter. Thisinvolves the study of field theory at finite temperature and withchemical potentials for appropriate charges, described in spacetime bycharged black hole solutions. The use of holography to study thesesystems requires a significant extrapolation, from the field theorieswhere classical gravitational calculations in the bulk are a usefulapproximation to the experimentally relevant theories. Nonetheless,the approach has had some striking qualitative successes, includingthe construction of holographic versions of superconducting orsuperfluid phase transitions, the identification of Fermi liquids witha variety of thermal behaviours, and the construction of a map betweena class of gravity solutions and the hydrodynamic regime in the fieldtheory. The use of holography provides a qualitatively new perspectiveon these aspects of strong coupling dynamics.In addition to insight into the behaviour of the strongly coupledfield theories, this work has led to new insights into the bulkdynamics and a deeper understanding of holography. The purpose of thisfocus issue is to strengthen the connections between this directionand other gravitational research and to make the gravity communitymore aware of these developments. The issue is made up of originalresearch contributions at the forefront of this area, giving a senseof the range of activity and presenting significant new contributions.Simon F Ross Guest Editor