| Abstract: | Condensed matter systems realize a great variety of interesting phases with exotic low energy excitations. Surprisingly, many of these were first envisioned in abstract quantum fields theories or particle physics. Prominent examples include relativistic electrons in graphene, or skyrmions that are observed in certain magnets. Another platform for novel phases was recently discovered in the form of 3D topological insulators, whose surfaces host isolated electronic Dirac cones protected by time reversal symmetry and charge conservation. Attractive interactions between these surface electrons can induce a unique superconducting state that hosts exotic excitations: Majorana quasiparticles.
In my talk, I will describe how strong interactions can instead drive these surfaces into symmetry-preserving states with surprising properties. For example, electrons may be stripped of their charge to form `composite Dirac liquids' with metallic thermal transport despite being electrical insulators. The study of these states has recently led to the remarkable proposal that non-interacting topological insulator surfaces can alternatively be described by quantum electrodynamics in (2+1) dimensions, where charge neutral 'dual fermions' strongly couple to an emergent photon. I will explain the origin of this surprising relationship and its implications for topological insulators, and for the theory of the half-filled Landau level in quantum Hall systems.
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