Strongly coupled physics from the gauge gravity duality

Abstract

The gauge/gravity duality links the fields of string theory and quantum field theory. The duality states that systems that are strongly coupled in one theory are weakly coupled in the other. Thus, intractable problems in strongly coupled physics can instead be calculated using the gravity side of the duality. In this thesis we study three areas of strongly coupled physics: quantum chromodynamics, condensed matter theory and (non)-hydrodynamic physics. First, we study quantum chromodynamics (QCD), where we attempt to gain insight into the temperature chemical potential QCD phase diagram by extending an exactly soluble holographic model into imaginary chemical potential. We then look for structure at small real µ and imaginary µ that help to reconstruct the large real µ phase diagram. We find that the phase diagram has boundaries of regions where metastable vacua exist and these boundaries, as well as the phase boundaries, converge at the holographic QCD critical point. We then move on to condensed matter theory where we study a top-down holographic Weyl semi-metal where we find the defining characteristic of a Weyl semi-metal: a quantum phase transition from a topological state with non-zero anomalous Hall conductivity to a trivial insulator. Unlike previous models, we find that the anomalous Hall conductivity is independent of model parameters at zero temperature and is also first order. At non-zero temperature the transition remains first order, and the anomalous Hall conductivity acquires non-trivial dependence on model parameters. Finally, we study the transition between non-hydrodynamic modes and hydrodynamic modes in holographic strange metals, where the microscopic description of the collective excitations is unknown but departs from the standard weakly-coupled Fermi liquid theory. We find that by including translational symmetry breaking the propagating non-hydrodynamic modes are damped, until at sufficiently large symmetry breaking parameters the mode transitions to the purely imaginary diffusive hydrodynamic mode.

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