Fractions: exotic new phases of matter

Abstract: Fracton phases are extremely unusual quantum phases of matter whose existence has only been recognized within the last decade or so. They host quasiparticles that, unlike electrons in metals, cannot move in all directions of space unless they move in concert with other quasiparticles which may be very far away. This movement restriction does not occur simply for energetic reasons; instead, it arises from more fundamental restrictions like exotic conservation laws or the structure of operators in the Hilbert space. I will give an overview of these bizarre and exciting phases of matter and discuss the ways in which they deeply challenge our understanding of field theory, gauge theory, and what a phase of matter even is.