UBC Theses and Dissertations
Baryons, branes, and (striped) black holes : applications of the gauge / gravity duality to quantum chromodynamics and condensed matter physics Stang, Jared Brendan
The gauge / gravity duality, or holographic correspondence, is a theoretical tool that allows the description of strongly coupled field theory through a dual classical gravity theory. In this thesis, we advance the use of numerical methods in applications of the holographic correspondence to the study of strongly coupled field theories in three situations. Firstly, we study the relationship between chemical potential and charge density across myriad examples of Lorentz invariant 3+1 dimensional holographic field theories with the minimal structure of a conserved charge. Solving for the classical gravitational configurations dual to the field theories and extracting the charge density and chemical potential, we enumerate the relationships that can exist in a wide range of holographic theories. Secondly, we study the spontaneous formation of inhomogeneous (striped) order, a phenomenon that has been observed in the cuprates, in a 2+1 dimensional strongly coupled field theory. By numerically solving the equations of motion using finite difference techniques, we construct the full nonlinear striped black brane solutions that provide the gravity dual to this field theory. We evaluate the thermodynamics and show that the system undergoes a second order phase transition to the striped phase as the temperature is lowered. Finally, we apply the holographic correspondence to study particular aspects of quantum chromodynamics (QCD). First, we develop a phenomenological holographic model to describe the colour superconductivity phase of QCD, which is believed to exist at large quark density. We construct the phase diagram for our model, which includes confined, deconfined, and superconducting phases. In a separate project, we revisit the construction of the baryon in the Sakai-Sugimoto model of holographic QCD. In this model, gauge field configurations on the probe D8 flavour branes with non-trivial topological charge (instantons) correspond to baryons in the dual field theory. In order to extend previous studies, we relax an assumption of spherical symmetry and, utilizing pseudospectral methods, numerically construct the deformed instanton in the bulk. Compared to previous studies, we find significantly more realistic values for the mass and size of the baryon.
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