One of my most rewarding activities last spring was serving as the teaching assistant for Mike Hopkins' course on algebraic topology and condensed matter. I learned so much from many wonderful conversations with Mike, and many incisive questions from students. Throughout the course, it became clear that invertible phases are an excellent entry into stable homotopy theory entirely on their own, and breath life into many of the key manipulations used in the subject. In this post, I want to emphasize one physical concept, the notion of a dielectric brane, which is quite familiar in string theory (and condensed matter, under different names). Hopefully, I'll convey the intuitive, almost tactile understanding of dielectric branes that has helped me enormously in understanding stable homotopy theory in general. To explain dielectric branes, we should first review conventional dielectrics. A dielectric is an insulating material with the following property: when you place it in an e...
A blog on quantum gravity, algebraic topology, condensed matter, and whatever else I'm thinking about.