  Dualities provide deep insight into physics by relating two seemingly
distinct theories. Here we consider a duality between lattice fermions and
bosons in (2+1) spacetime dimensions, relating free massive Dirac fermions to
Abelian Chern-Simons Higgs (ACSH) bosons. To establish the duality we represent
the exact partition function of the lattice fermions in terms of the writhe of
fermionic worldlines. On the bosonic side the partition function is expressed
in the writhe of the vortex loops of the particle-vortex dual of the ACSH
Lagrangian. In the continuum and scaling limit we show these to be identical.
This result can be understood from the closed fermionic worldlines being direct
mappings of the ACSH vortex loops, with the writhe keeping track of particle
statistics.
