Algebraic vortex liquid in spin-1/2 triangular antiferromagnets: Scenario for Cs$_2$CuCl$_4$

Motivated by inelastic neutron scattering data on Cs$_2$CuCl$_4$, we explore spin-1/2 triangular lattice antiferromagnets with both spatial and easy-plane exchange anisotropies, the latter due to an observed Dzyaloshinskii-Moriya interaction. Exploiting a duality mapping followed by a fermionization of the dual vortex degrees of freedom, we find a novel ``critical" spin-liquid phase described in terms of Dirac fermions with an emergent global SU(4) symmetry minimally coupled to a non-compact U(1) gauge field. This ``algebraic vortex liquid" supports gapless spin excitations and universal power-law correlations in the dynamical spin structure factor which are consistent with those observed in Cs$_2$CuCl$_4$. We suggest future neutron scattering experiments that should help distinguish between the algebraic vortex liquid and other spin liquids and quantum critical points previously proposed in the context of Cs$_2$CuCl$_4$.