  We study the effects of a small density of holes, delta, on a square lattice
antiferromagnet undergoing a continuous transition from a Neel state to a
valence bond solid at a deconfined quantum critical point. We argue that at
non-zero delta, it is likely that the critical point broadens into a non-Fermi
liquid `holon metal' phase with fractionalized excitations. The holon metal
phase is flanked on both sides by Fermi liquid states with Fermi surfaces
enclosing the usual Luttinger area. However the electronic quasiparticles carry
distinct quantum numbers in the two Fermi liquid phases, and consequently the
limit of the ratio A_F/delta, as delta tends to zero (where A_F is the area of
a hole pocket) has a factor of 2 discontinuity across the quantum critical
point of the insulator. We demonstrate that the electronic spectrum at this
transition is described by the `boundary' critical theory of an impurity
coupled to a 2+1 dimensional conformal field theory. We compute the finite
temperature quantum-critical electronic spectra and show that they resemble
"Fermi arc" spectra seen in recent photoemission experiments on the pseudogap
phase of the cuprates.
