Gauge/gravity duality applied to condensed matter systems

In this review we investigate phenomena of strongly‐coupled quantum critical theories, which also appear in condensed matter systems. Using the AdS/CFT correspondence, a technique motivated by string theory, the strongly‐coupled scale‐invariant theories can be related to gravity theories at weak coupling. Within this framework we study the holographic description of superconductors and the emerging fermi surface of strongly coupled fermions. We also calculate the conductivity of alternating currents and determine the direct current conductivity for (non‐) relativistic systems beyond linear response. Since the explicit string theory construction in terms of probe branes embedded in type IIB supergravity is explicitly known, we are able to identify the dual operators on the field theory side and can compare the effects at weak and strong coupling. In this review we investigate phenomena of strongly‐coupled quantum critical theories, which also appear in condensed matter systems. Using the AdS/CFT correspondence, a technique motivated by string theory, the strongly‐coupled scale‐invariant theories can be related to gravity theories at weak coupling. Within this framework we study the holographic description of superconductors and the emerging fermi surface of strongly coupled fermions. We also calculate the conductivity of alternating currents and determine the direct current conductivity for (non‐) relativistic systems beyond linear response. Since the explicit string theory construction in terms of probe branes embedded in type IIB supergravity is explicitly known, we are able to identify the dual operators on the field theory side and can compare the effects at weak and strong coupling.