  Gauge/Gravity dualities open the non-perturbative realms of strongly-coupled
gauge theories to analytic treatment. Anti-de Sitter Space/Conformal Field The-
ory, one way of connecting gravity dual models to gauge theories, is a
correspon- dence between a ten-dimensional Type IIB superstring theory in AdS5
\times S 5 and a N = 4 super Yang Mills theory. To describe systems that are
experimentally ac- cessible, 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 rela- tion
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.
