  In this thesis, we study a variety of phenomena in strongly coupled quantum
field theories by performing calculations in their gravitational duals. We
compute entanglement entropy in a variety of holographic systems, paying
particular attention to its long-distance behaviour, characterised by a term
proportional to surface area. This term is known to decrease along
Lorentz-invariant renormalisation group flows, suggesting that it may count
massless degrees of freedom. We find that more general deformations may
increase this area term, possibly indicating an enhanced number of
long-distance degrees of freedom. We observe a correlation between this
enhancement and the emergence of new scaling symmetry at long distances. Next,
we study the spectrum of collective excitations in a holographic model of a
non-Fermi liquid. At high temperatures, the spectrum of collective excitations
includes hydrodynamic sound waves. As in similar models, we observe that
sound-like modes also exist at low temperatures. Such modes are known as
holographic zero sound. We study the changing properties of holographic zero
sound and the emergence of hydrodynamic behaviour at high temperatures as we
vary the parameters of the model. We find that for certain values of the
parameters, the temperature-dependence of holographic zero sound qualitatively
resembles that of a normal Fermi liquid. Finally, we study the entanglement
entropy contribution of surface defects in a six-dimensional quantum field
theory of relevance to M-theory, which is a candidate theory of quantum
gravity. We find that the entanglement entropy does not montonically decrease
along renormalisation group flows on these defects, ruling it out as a
potential measure of degrees of freedom. On the other hand, we find that two of
the contributions of the defect to the Weyl anomaly of the quantum field theory
decrease along all of the flows that we study.
