Twistorial and space-time descriptions of D=4 string models

We derive twistorial tensionful bosonic string action by considering on the world sheet the canonical twistorial 2-form in two-twistor space. We demonstrate the equivalence of or model to two known momentum formulations of D=4 bosonic string, with covariant worldsheet vectorial string momenta $P_\mu^m(\tau,\sigma)$ and the one with tensorial string momenta $P_{[\mu\nu]}(\tau,\sigma)$. All considered here string actions, in twistorial and mixed spinor-spacetime formulations, are classically equivalent to the Nambu-Goto action.