Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions

Abstract

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED${}_3$) with $N=1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED${}_3$ scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and $N=2$ QED${}_3$.

15 pages, 5 figures; added appendix on constructions in strict 2D and properties of N=1 QED3