  We compute the electronic Green's function of the topologically ordered Higgs
phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square
lattice. The results are compared with cluster extensions of dynamical mean
field theory, and quantum Monte Carlo calculations, on the pseudogap phase of
the strongly interacting hole-doped Hubbard model. Good agreement is found in
the momentum, frequency, hopping, and doping dependencies of the spectral
function and electronic self-energy. We show that lines of (approximate) zeros
of the zero-frequency electronic Green's function are signs of the underlying
topological order of the gauge theory, and describe how these lines of zeros
appear in our theory of the Hubbard model. We also derive a modified,
non-perturbative version of the Luttinger theorem that holds in the Higgs
phase.
