The effect of velocity anisotropy on the antiferromagnetic instability of a d-wave superconductor

We consider the effective 2+1 dimensional electrodynamics (QED_3) of low-energy quasiparticles coupled to fluctuating vortex loops in the d-wave superconductor, with the velocity anisotropy: v_F not equal to v_Delta. This theory should be relevant to the quantum superconductor-insulator transition in underdoped cuprates. Working in the customary large-N approximation, we find that weak anisotropy is a marginally irrelevant perturbation to the Lorentz invariant QED_3, and that the critical number N_c of Dirac fields below which the theory suffers the antiferromagnetic (chiral) instability stays the same.