We introduce polarization field displays as an optically efficient design for dynamic light field display using multi-layered LCDs. Such displays consist of a stacked set of liquid crystal panels with a single pair of crossed linear polarizers. Each layer is modeled as a spatially controllable polarization rotator, as opposed to a conventional spatial light modulator that directly attenuates light. We demonstrate that such displays can be controlled, at interactive refresh rates, by adopting the SART algorithm to tomographically solve for the optimal spatially varying polarization state rotations applied by each layer. We validate our design by constructing a prototype using modified off-the-shelf panels. We demonstrate interactive display using a GPU-based SART implementation supporting both polarization-based and attenuation-based architectures.