  The quantum phase transitions of metals have been extensively studied in the
rare-earth "heavy electron" materials, the cuprates, and related compounds. The
Fermi surface of the metal often has different shapes in the states well away
from the critical point. It has been proposed that these differences can
persist up to the critical point, setting up a discontinuous Fermi surface
change across a continuous quantum transition. We study square lattice
antiferromagnets undergoing a continuous transition from a Neel state to a
valence bond solid, and examine the fate of a small density of holes in the two
phases. Fermi surfaces of charge e, spin 1/2 quasiparticles appear in both
phases, enclosing the usual Luttinger area. However, additional quantum numbers
cause the area enclosed by each Fermi surface pocket to jump by a factor of 2
across the transition in the limit of small density. We demonstrate that the
electronic spectrum across this transition is described by a critical theory of
a localized impurity coupled to a 2+1 dimensional conformal field theory. This
critical theory also controls the more complex Fermi surface crossover at fixed
density, which likely involves intermediate phases with exotic fractionalized
excitations. We suggest that such theories control the electronic spectrum in
the pseudogap phase of the cuprates.
