  We examine the quantum theory of the spontaneous breaking of lattice rotation
symmetry in d-wave superconductors on the square lattice. This is described by
a field theory of an Ising nematic order parameter coupled to the gapless
fermionic quasiparticles. We determine the structure of the renormalization
group to all orders in a 1/N_f expansion, where N_f is the number of fermion
spin components. Asymptotically exact results are obtained for the quantum
critical theory in which, as in the large N_f theory, the nematic order has a
large anomalous dimension, and the fermion spectral functions are highly
anisotropic.
