  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.
