| Summary: | This thesis investigates a number of topics relating to flavour physics and entanglement within gauge/gravity duality, or ‘holography’, which is a framework for studying equivalences between certain gravitational and non-gravitational theories. The field arose from generalisations of the original AdS/CFT correspondence, which postulated the equivalence between the N = 4 super Yang-Mills gauge theory and type IIB superstring theory on AdS5 × S5. The duality is such that the gauge theory is strongly-coupled when the string theory reduces to a classical supergravity theory, and consequently provides a new method of computation for strongly coupled physics such as QCD and many condensed matter systems. In this thesis we study applications of gauge/gravity duality to flavour physics, and both applications and fundamental issues of entanglement within the holographic framework. We study a holographic model of graphene in a cavity and find a new controlled example of mass gap generation, and a new phase in which a graphene sheet condenses with its mirror image. We then study a bottom-up model known as Dynamic AdS/QCD, and reproduce soft wall behaviour needed to obtain the known Regge behaviour for meson masses, discussing some inherent limitations in the approach. The discussion then moves onto the entanglement of flavour in AdS/CFT, and we compute the entanglement entropy in detail for the massive D3/D7 system, and present a new method for computing the entanglement entropy of any top-down brane probe system using Kaluza-Klein holography. Finally, we study the issue of entanglement entropy in generic top-down models, and provide strong evidence that it can be computed via a generalisation of the Ryu-Takayanagi formula, using codimension two minimal surfaces which asymptotically wrap the compact part of the geometry.
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