  Several recent works on quantum criticality beyond the Landau-Ginzburg-Wilson
paradigm have led to a number of field theories, potentially important for
certain two-dimensional magnetic insulating systems, where criticality is not
very well understood. This situation highlights the need for non-perturbative
information about criticality in two spatial dimensions (three space-time
dimensions), which is a longstanding challenge. As a step toward addressing
these issues, we present evidence that the O(4) vector model is dual to a
theory of Dirac fermions coupled to both SU(2) and U(1) gauge fields. Both
field theories arise as low-energy, long-wavelength descriptions of a
frustrated XY model on the triangular lattice. Abelian boson-vortex duality of
the lattice model, together with the emergence of larger non-abelian symmetry
at low energies, leads to this rare example of duality in two spatial
dimensions involving non-abelian global symmetry and fermions, but without
supersymmetry. The duality can also be viewed as a bosonization of the Dirac
fermion gauge theory.
