Exact bosonization in two and three spatial dimensions and new classes of lattice gauge theory

We will describe 2d (3d) analogs of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d (3d) lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. The lattice gauge theory can be understood us a stabilizer code. When the space is simply-connected, this bosonization map is an equivalence. On 2d square lattice, our bosonization mapping is equivalent to Bravyi-Kitaev "Superfast simulation of Fermions" and it has possible applications on quantum simulation of fermions. We also describe Euclidean actions for the corresponding lattice gauge theories and find that the (2+1)D theory contains Chern-Simons-like terms, which can be considered as Z/2Z version of particle-vortex duality.