Holographic Duality and Strongly Interacting Quantum Matter
Typ
Examensarbete för masterexamen
Program
Physics and astronomy (MPPAS), MSc
Publicerad
2020
Författare
Lassila, Marcus
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.