  We describe a 2d analog of the Jordan-Wigner transformation which maps an
arbitrary fermionic system on a 2d lattice to a lattice gauge theory while
preserving the locality of the Hamiltonian. When the space is simply-connected,
this bosonization map is an equivalence. We describe several examples of 2d
bosonization, including free fermions on square and honeycomb lattices and the
Hubbard model. We describe Euclidean actions for the corresponding lattice
gauge theories and find that they contains Chern-Simons-like terms. Finally, we
write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker
model).
