Holographic Duality and Strongly Interacting Quantum Matter
Examensarbete för masterexamen
This thesis is devoted to the applications of holographic duality to condensed matter physics. It is centered around a ‘bottom-up’ approach where the starting point is the postulation of a reasonable gravitational bulk theory action, as opposed to the ‘top-down’ models where a specific duality is derived from a string theory setting. The main motivation for taking a holographic approach to condensed matter physics is the potential ability to perform reliable computations for strongly interacting quantum many-body systems, in the absence of a quasiparticle description. The duality maps a strongly coupled quantum field theory to a weakly interacting gravitational theory, which in principle can be solved perturabtively using ordinary general relativity. An introduction to some of the main topics of bottom-up holography is given. This includes a brief introduction to large N field theories, the AdS/CFT correspondance, the holographic dictionary, the holographic renormalization group, holographic thermodynamics, and the Hawking-Page transition and its interpretation in the light of AdS/CFT. Finally, a minimal bottom-up toy model for holographic superconductivity is studied. By imposing a mixed boundary condition at the boundary of AdS space, a dynamical photon is incorporated in the strongly coupled superconductor. This allows charged collective excitations, e.g. plasmons, to be studied. A linear response analysis of the minimal holographic superconductor is performed numerically, in an attempt to compute plasmon dispersion relations. It turns out that the mixed boundary condition, accounting for charged collective excitations, will likely have to be modified for this particular holographic superconductor model, since the computed plasmon dispersion relation indicates an instability at large momenta. The precise way in which the mixed boundary condition has to be modified remains unclear.