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 antinodal 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 CP1 theory of spinons. This theory leads to metals with an antinodal gap and topological order which intertwines with the observed broken symmetries.