An integrated kinetics-based Large Eddy Simulation (LES) approach for soot evolution in turbulent reacting flows is applied to the simulation of a Pratt & Whitney aircraft gas turbine combustor, and the results are analyzed to provide insights into the complex interactions of the hydrodynamics, mixing, chemistry, and soot. In the integrated approach, the soot model is based on the Hybrid Method of Moments (HMOM) and detailed descriptions of the various chemical and physical microprocesses governing soot evolution. The detailed kinetics of jet fuel oxidation and soot precursor formation are described with the Radiation Flamelet/Progress Variable (RFPV) model, which has been modified to account for the slow chemistry governing Polycyclic Aromatic Hydrocarbons (PAH) and the removal of these species from the gas-phase to form soot. The filtered transport equations in the soot and combustion models are closed with a presumed subfilter PDF approach that accounts for the unresolved scalar mixing as well as the small-scale, high intermittency characteristic of soot. These models are combined with a Lagrangian description of the liquid fuel spray and state-of-the-art unstructured LES technology for complex geometries in order to simulate the combustor at two different overall equivalence ratios. Qualitatively, soot is present in very large quantities in the recirculation zone in the primary zone of the combustor where the mixture fraction is rich. Downstream of the introduction of dilution air, soot is quickly oxidized as regions of rich mixture fraction are rapidly mixed out. As the overall equivalence ratio is increased, the dominant soot growth process transitions from acetylene-based surface growth at lower mixture fractions to PAH-based condensation at higher mixture fractions. Quantitatively, the model overpredicts the soot volume fraction at the exit plane of the combustor by about 50% at both equivalence ratios, and the ratio in exit smoke number between two different overall equivalence ratios is predicted very well by the simulations compared to experimental measurements.