  We revisit two-dimensional frustrated quantum magnetism from a new
perspective, with the aim of exploring new critical points and critical phases.
We study easy-plane triangular antiferromagnets using a dual vortex approach,
fermionizing the vortices with a Chern-Simons field. Herein we develop this
technique for integer-spin systems which generically exhibit a simple
paramagnetic phase as well as magnetically-ordered phases with coplanar and
collinear spin order. Within the fermionized-vortex approach, we derive a
low-energy effective theory containing Dirac fermions with two flavors
minimally coupled to a U(1) and a Chern-Simons gauge field. At criticality we
argue that the Chern-Simons gauge field can be subsumed into the U(1) gauge
field, and up to irrelevant interactions one arrives at quantum electrodynamics
in (2+1) dimensions (QED3). Moreover, we conjecture that critical QED3 with
full SU(2) flavor symmetry describes the O(4) multicritical point of the spin
model where the paramagnet and two magnetically-ordered phases merge. The
remarkable implication is that QED3 with flavor SU(2) symmetry is dual to
ordinary critical Phi^4 field theory with O(4) symmetry. This leads to a number
of unexpected, verifiable predictions for QED3. A connection of our
fermionized-vortex approach with the dipole interpretation of the nu=1/2
fractional quantum Hall state is also demonstrated. The approach introduced in
this paper will be applied to spin-1/2 systems in a forthcoming publication.
