Kelley, Thomas Matthew2011-08-172011-08-172011-07https://hdl.handle.net/11299/113168University of Minnesota Ph.D. dissertation. July 2011. Major:Physics. Advisors: Tony Gherghetta and Joe Kapusta. 1 computer file (PDF); ix, 142 pages, appendix A.Gauge/Gravity dualities open the non-perturbative realms of strongly-coupled gauge theories to analytic treatment. Anti-de Sitter Space/Conformal Field Theory, one way of connecting gravity dual models to gauge theories, is a correspondence between a ten-dimensional Type IIB superstring theory in $AdS_{5}\times S^{5}$ and a $\mathcal{N}=4$ super Yang Mills theory. To describe systems that are experimentally accessible, however, the formal correspondence is modified into a phenomenological duality between a five-dimensional gravity model and a strongly coupled QCD-like gauge theory. This duality is referred to as AdS/QCD. This work explores aspects of the soft-wall AdS/QCD model. The phrase `soft wall' refers to the means of breaking the conformal symmetry and introducing a mass scale to the gauge side of the duality. We add higher-order terms to the soft-wall Lagrangian and calculate the effect on physical observables. Meson mass spectra gain a more complex structure, exhibiting a better match with the experimental values than previous models. The Gell-Mann--Oakes--Renner relation naturally emerges from the model. We calculate the form factor $F_{\pi}$ and the coupling $g_{\rho\pi\pi}$ as a non-trivial test on the limits of our soft-wall model. Introducing a black brane into the gravity dual metric allows us to derive thermodynamic quantities in the gauge theory. As expected at high temperatures, the entropy scales as the cube of the temperature, and the speed of sound reaches its conformal limit of one-third. Thermal condensates contribute leading-order terms, modifying the temperature, entropy, and free energy behavior. We find that the system undergoes a phase transition from hadronic matter to a strongly coupled quark-gluon plasma at a critical temperature.en-USAdS/CFTAdS/QCDGauge/gravity dualitiesQCD ThermodynamicsSoft-WallPhysicsThesis or Dissertation