  We study the dynamics of topological defects of a frustrated spin system
displaying spiral order. As a starting point we consider the SO(3) nonlinear
sigma model to describe long-wavelength fluctuations around the noncollinear
spiral state. Besides the usual spin-wave magnetic excitations, the model
allows for topologically non-trivial static solutions of the equations of
motion, associated with the change of chirality (clockwise or counterclockwise)
of the spiral. We consider two types of these topological defects, single
vortices and vortex-antivortex pairs, and quantize the corresponding solutions
by generalizing the semiclassical approach to a non-Abelian field theory. The
use of the collective coordinates allows us to represent the defect as a
particle coupled to a bath of harmonic oscillators, which can be integrated out
employing the Feynman-Vernon path-integral formalism. The resulting effective
action for the defect indicates that its motion is damped due to the scattering
by the magnons. We derive a general expression for the damping coefficient of
the defect, and evaluate its temperature dependence in both cases, for a single
vortex and for a vortex-antivortex pair. Finally, we consider an application of
the model for cuprates, where a spiral state has been argued to be realized in
the spin-glass regime. By assuming that the defect motion contributes to the
dissipative dynamics of the charges, we can compare our results with the
measured inverse mobility in a wide range of temperature. The relatively good
agreement between our calculations and the experiments confirms the possible
relevance of an incommensurate spiral order for lightly doped cuprates.
