Abstract:
Despite several efforts, strongly correlated systems still pose as one of the most challenging
conundrums in theoretical physics. The difficulty in modelling and solving the problems
has grown even more after the discovery of high-temperature superconductors, topological
insulators, Dirac and Weyl’s semimetals. Experimental results on these materials have
revealed many intriguing phenomena such as pseudo-gap phase and Fermi arcs, which
we have very little understanding theoretically. These systems are not suitable to be
described by conventional perturbative approaches. In the present thesis, we used an
alternative method with a non-perturbative tool provided by the gauge-gravity duality,
allowing us to access the strongly coupled regime.
With the motivation to understand the underlying mechanism that gives rise to these
peculiar phenomena, we proposed several holographic models by exploring the symmetries
of either the background geometry in the bulk or at the boundary. By computing the
fermions spectral function, we primarily explore the properties of the Fermi surface and
Fermi arcs in certain strongly coupled systems of interests. Our results revealed some
interesting features that are closely related to those that are seen in real materials from
condensed matter experiments
