  We study the spin dynamics in underdoped cuprates at low temperatures by
considering them as quasi two dimensional d-wave superconductors (dSC) with
strong phase fluctuations. An effective theory of spin degrees of freedom of
nodal quasiparticles coupled to vortex defects in the phase of the
superconducting order parameter is formulated. It represents the minimal
extension of the QED3 theory of the pseudogap phase into the superconducting
region. The theory predicts a single dSC-SDW transition, which may be
fluctuation induced first order, without the region of coexistence between the
two ordered phases. We compute the spin-spin correlator in the dSC, and explain
the evolution of the spin response with frequency as observed in neutron
scattering experiments on YBCO. We predict that at the frequencies much below
the resonance the (weak) spin response should become narrowly peaked at four
`diagonally' incommensurate wave vectors that span between the nodes of the
supercopnducting order parameter. These peaks represent an inherent collective
mode of the phase fluctuating dSC, the condensation of which would bring about
the SDW order in the pseudogap phase. Our interpretation of the resonance
suggests it should become more elusive in the superconductors with lower Tc, in
accord with its' conspicuous absence in LSCO.
