To define a consistent perturbative geometric heterotic compactification the bundle is required to satisfy a subtle constraint known as “stability,” which depends upon the Kähler form. This dependence upon the Kähler form is highly nontrivial – the Kähler cone splits into subcones, with a distinct moduli space of bundles in each subcone – and has long been overlooked by physicists. In this arti...

Mass clumps in gravitational lens galaxies can perturb lensed images in characteristic ways. Strong lens flux ratios have been used to constrain the amount of dark matter substructure in lens galaxies, and various other observables have been considered as additional probes of substructure. We study the general theory of lensing with stochastic substructure in order to understand how lensing obs...