Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Abstract

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless 2-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly non-trivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a non-perturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

v2: typos fixed, some discussions clarified