Last Friday, I had the opportunity to give a very fun talk at the MIT student journal club on our Baby Universe Hypothesis . A major theme of the talk, and the resulting discussion, was that holography isn't free! In many ways, this is the heart of the Swampland: if you just throw whatever junk you want into the Euclidean path integral, there's really no reason to expect anything but junk out the other end. This is strikingly different from quantum field theory, where (up to canceling anomalies) you are free to write down whatever you wish. In this post, I want to share some observations that make this difference between gravity and other quantum systems more obvious, as well as point the way towards the type of mathematical structure we need in order to guarantee holography. The miracle of holography, and the true heart of the issue, is not that a bulk gravitational system becomes a quantum system on the boundary, but rather that it becomes a local quantum system on the bound
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 el