Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Understand

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.