Twistors and actions on coset manifolds

Particle and string actions on coset spaces typically lack a quadratic kinetic term, making their quantization difficult. We define a notion of twistors on these spaces, which are hypersurfaces in a vector space that transform linearly under the isometry group of the coset. By associating the points of the coset space with these hypersurfaces, and the internal coordinates of these hypersurfaces with momenta, it is possible to construct manifestly symmetric actions with leading quadratic terms. We give a general algorithm and work out the case of a particle on ${\mathrm{AdS}}_p$ explicitly. In this case, the resulting action is a world-line gauge theory with sources (the gauge group depending on $p),$ which is equivalent to a nonlocal world-line $\sigma$ model.