Fivebranes and Fractons

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

This week, during the first Swampland open mic event, there was a lot of discussion about the role of duality in quantum gravity, and in particular the appearance of light extended objects of various dimensions: particles, strings, and possibly membranes. Many facets of this question were discussed, including how to understand which objects appear at which infinite-distance limit in moduli space, the structure of theories with various numbers of supercharges, and light towers of objects which are not the lightest in the theory. I made some comments about where I think we should look for answers, but I'm sure those comments were close to unintelligible, as my thoughts are nowhere close to organized. In this blog post, I want to start describing the free associations that suggest, to me, the answers lie in chromatic homotopy theory. If you haven't heard of chromatic homotopy theory, don't panic, since I'm mostly going to parrot words I've heard with no real comprehens

I've been thinking of starting a blog for a while, but the real catalyst was some recent discussions about my paper " Baby Universes, Holography, and the Swampland " with Cumrun Vafa. Based on these discussions, I think some less-directed rambling might help to clarify our perspective, and so I've decided to start this blog! With no real plans for how frequently I'm going to post, keep your expectations low, but I feel like there are ideas about physics that don't fit neatly into a paper, so I hope to continue sharing them here. To get into it, what, exactly, are we claiming in this paper? The central physical claim is the following hypothesis: In a consistent and complete theory of quantum gravity, the Hilbert space of baby universe states is one-dimensional. As an aside, I prefer the word "hypothesis" to "conjecture" for most Swampland conditions; to me, a conjecture is a precise claim about a well-defined mathematical structure, which is