  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.
