Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions

We study the stability of the 2+1 dimensional U(1) spin liquid state against proliferation of instantons in the presence of spinon Fermi surface. By mapping the spinon Fermi surface into an infinite set of 1+1 dimensional chiral fermions, it is argued that an instanton has an infinite scaling dimension for any nonzero number of spinon flavors. Therefore, the spin liquid phase is stable against instantons and the non-compact U(1) gauge theory is a good low energy description.