Atomic and electronic structures as well as ferroelectricity at Σ5(001) twist boundaries in ferroelectric PbTiO_{3} have been investigated using first-principles (ab initio) density-functional theory calculations within the local-density approximation. The twist-boundary structure with the coincidence site lattice of O-Pb and O-O is found to be energetically favorable. At the twist boundary, rectilinear spontaneous polarization along the normal direction to the boundary is highly enhanced because of the locally strengthened covalent Pb-O bond, which predominates ferroelectricity in PbTiO_{3}. Interestingly, we found vortex or toroidal polarization in the twist-boundary plane coexisting with the rectilinear polarization. The vortex polarization arises from rotational in-plane displacement induced by the twisted misorientation of lattices. An applied tensile strain tends to increase the rectilinear polarization, especially at the twist boundary. On the other hand, the vortex polarization is suppressed upon application of a tensile strain and finally disappears at a critical strain in the TiO_{2} layer of the boundary, whereas the PbO layer exhibits the opposite tendency.
