  A d-wave superconductor, subject to strong phase fluctuations, is known to
suffer an antiferromagnetic instability closely related to the chiral symmetry
breaking in (2+1)-dimensional quantum electrodynamics (QED3). On the basis of
this idea we formulate a "QED3 in a box" theory of local instabilities of a
d-wave superconductor in the vicinity of a single pinned vortex undergoing
quantum fluctuations around its equilibrium position. As a generic outcome we
find an incommensurate 2D spin density wave forming in the neighborhood of a
vortex with a concomitant "checkerboard" pattern in the local electronic
density of states, in agreement with recent neutron scattering and tunneling
spectroscopy measurements.
