Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the `anti-nodal’ region of the square lattice Brillouin zone, and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin density wave mean field theory of the square lattice Hubbard model, and in a CP${}^1$ theory of spinons. This theory leads to metals with an antinodal gap, and topological order which intertwines with precisely the observed broken symmetries.