  We present a theoretical study of two-dimensional spatially and temporally
varying magnetic textures in the presence of spin-orbit coupling (SOC) of both
the Rashba and Dresselhaus types. We show that the effective gauge field due to
these SOCs, contributes to the dissipative and reactive spin torques in exactly
the same way as in electromagnetism. Our calculations reveal that Rashba
(Dresselhaus) SOC induces a chiral dissipation in interfacial (bulk) inversion
asymmetric magnetic materials. Furthermore, we show that in addition to chiral
dissipation $\alpha_c$, these SOCs also produce a chiral renormalization of the
gyromagnetic ratio $\tilde{\gamma}_c$, and show that the latter is
intrinsically linked to the former via a simple relation $\alpha_c =
(\tau/\tau_{\rm ex}) \tilde{\gamma}_c$, where $\tau_{\rm ex}$ and $\tau$ are
the exchange time and the electron relaxation time, respectively. Finally, we
propose a theoretical scheme based on the Scattering theory to calculate and
investigate the properties of damping in chiral magnets. Our findings should in
principle provide a guide for material engineering of effects related to chiral
dynamics in magnetic textures with SOC.
