| In this thesis we discuss spontaneous symmetry breaking in the context of the Anti-de Sitter/Conformal field theory (AdS/CFT) correspondence and interpret it as as a model of superconductivity or superfluidity in strongly coupled systems. After reviewing relevant aspects of the AdS/CFT correspondence and the standard Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, we investigate how spontaneous breaking of an abelian symmetry can occur in the context of AdS/CFT, a construction which is often called a "holographic superconductor,'' as in the spontaneously broken phase there is infinite DC electrical conductivity and a pronounced gap in the AC conductivity. We begin by working in the probe limit, where much of the analysis is simplified but we are unable to study the system at low temperatures. In this limit we study holographic s-wave superconductors and find remarkably general behavior for a wide class of theories. We next study p-wave holographic superconductors in the probe limit and find spontaneous time-reversal symmetry breaking and other interesting features. We then study the s-wave system away from the probe limit, analyze the zero temperature limit of these holographic superconductors, and find that despite having to rely on numerical methods for much of our work, we are able to deduce strong analytic results about the apparent gap in AC conductivity at zero temperature. We then study fermionic transport of the s-wave superconductors, in analogy to photoemission experiments on laboratory superconductors. We also discuss new developments which should allow us to further probe the exciting new developments connecting condensed matter physics and string theory. |
