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. The integrated approach includes detailed models for soot, combustion, and the unresolved interactions between soot, chemistry, and turbulence. The soot model is based on the Hybrid Method of Moments and detailed descriptions of soot aggregates and the various physical and chemical processes governing their evolution. The detailed kinetics of jet fuel oxidation and soot precursor formation is described with the Radiation Flamelet/Progress Variable model, which has been modified to account for the removal of soot precursors from the gas-phase. The unclosed filtered quantities in the soot and combustion models, such as source terms, are closed with a novel presumed subfilter PDF approach that accounts for the high subfilter spatial intermittency of soot. For the combustor simulation, the integrated approach is combined with a Lagrangian parcel method for the liquid spray and state-of-the-art unstructured LES technology for complex geometries. Two overall fuel-to-air ratios are simulated to evaluate the ability of the model to make not only absolute predictions but also quantitative predictions of trends. The Pratt & Whitney combustor is a Rich-Quench-Lean combustor in which combustion first occurs in a fuel-rich primary zone characterized by a large recirculation zone. Dilution air is then added downstream of the recirculation zone, and combustion continues in a fuel-lean secondary zone. The simulations show that large quantities of soot are formed in the fuel-rich recirculation zone, and, furthermore, the overall fuel-to-air ratio dictates both the dominant soot growth process and the location of maximum soot volume fraction. At the higher fuel-to-air ratio, the maximum soot volume fraction is found inside the recirculation zone; at the lower fuel-to-air ratio, turbulent fluctuations in the mixture fraction promote the oxidation of soot inside the recirculation zone and suppress the accumulation of a large soot volume fraction. Downstream, soot exits the combustor in intermittent fuel-rich pockets that are not mixed during the injection of dilution air and subsequent secondary fuel-lean combustion. At the higher fuel-to-air ratio, the frequency of these fuel-rich pockets is increased, leading to higher soot emissions from the combustor. Quantitatively, the soot emissions from the combustor are overpredicted by about 50%, which is a substantial improvement over previous works utilizing RANS to predict such emissions. In addition, the ratio between the two fuel-to-air ratios predicted by LES compares very favorably with the experimental measurements. Furthermore, soot growth is dominated by an acetylene-based pathway rather than an aromatic-based pathway, which is usually the dominant mechanism in nonpremixed flames. This finding is the result of the interactions between the hydrodynamics, mixing, chemistry, and soot in the recirculation zone and the resulting residence times of soot at various mixture fractions (compositions), which are not the same in this complex recirculating flow as in nonpremixed jet flames.