Exact bosonization in all dimensions and the duality between fermionic SPT and higher-group bosonic SPT phases
The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any manifold in 2d, 3d, and general dimensions. This gives a duality between all fermionic systems and a new class of Z2 lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action.