  Although magnetically ordered at low temperatures, the spin-1/2 triangular
antiferromagnet Cs_2CuCl_4 exhibits remarkable spin dynamics that strongly
suggest proximity to a spin liquid phase. Here we address the question of
whether a proximate spin liquid may also occur in an applied magnetic field,
leaving a similar imprint on the dynamical spin correlations of this material.
Specifically, we explore a spatially anisotropic Heisenberg spin-1/2 triangular
antiferromagnet at 1/3 magnetization from a dual vortex perspective, and indeed
find a new ``critical'' spin liquid phase described by QED3 with an emergent
SU(6) symmetry. A number of nontrivial predictions are given for the dynamical
spin structure factor in this ``algebraic vortex liquid'' phase, which can be
tested experimentally via inelastic neutron scattering. We also discuss how the
well-studied ``up-up-down'' magnetization plateaus can be captured within our
approach, and further predict the existence of a stable gapless solid phase in
a weakly ordered up-up-down state. Finally, we predict several anomalous
``roton'' minima in the excitation spectrum in the regime of lattice anisotropy
where the canted Neel state appears.
