There are a number of technical puzzles involved in understanding the relationship between stacks and gauged sigma models in physics. One such puzzle, of a more mathematical flavor, involves deformation theory. Specifically, although for sigma models on smooth spaces the physical deformations of the CFT match the mathematical deformations of the target space, for gauged sigma models there is a mismatch between physical deformations and mathematical deformations. In this talk we shall outline some work in progress on resolving such issues. Among other things, we will find that in order to understand mirror symmetry for stacks, one is led to a new class of abstract CFT's described by adding physical fields valued in roots of unity, something that to our knowledge has not been studied before in physics.