R-Charge Chemical Potential in a 2+1 Dimensional System

We study probe D5 branes in D3 brane AdS_5 and AdS_5-Schwarzschild backgrounds as a prototype dual description of strongly coupled 2+1 dimensional quasi-particles. We introduce a chemical potential for a weakly gauged U(1) subgroup of the theory's global R-symmetry by spinning the D5 branes. The resulting D5 embeddings are complicated by the existence of a region of the space in which the local speed of light falls below the rotation speed. We find regular embeddings through this region and show that the system does not exhibit the spontaneous symmetry breaking that would be needed for a superconductor.