Renormalization group theory of nematic ordering in d-wave superconductors

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 Nf theory, the, nematic order has a large anomalous dimension, and the fermion spectral functions are highly anisotropic.