Nodal quasiparticles and the onset of spin density wave order in the cuprates

We present a theory for the onset of spin density wave order in the superconducting ground state of the cuprates. We compute the scaling dimensions of allowed perturbations of a `relativistic' fixed point with O(4)xO(3) symmetry, including those associated with the fermionic nodal Bogoliubov quasiparticles. Analyses of up to six loops show that all perturbations with square lattice symmetry are likely irrelevant. We demonstrate that the fermion spectral functions are primarily damped by the coupling to fluctuations of a composite field with Ising nematic order. We also discuss the influence of quenched disorder.