Twistorial versus space--time formulations: unification of various string models

Abstract

We introduce the D=4 twistorial tensionfull bosonic string by considering the canonical twistorial 2--form in two--twistor space. We demonstrate its equivalence to two bosonic string models: due to Siegel (with covariant worldsheet vectorial string momenta $P_\mu^{m}(\tau,\sigma)$) and the one with tensorial string momenta $P_{[\mu\nu]}(\tau,\sigma)$. We show how to obtain in mixed space-time--twistor formulation the Soroka--Sorokin--Tkach--Volkov (SSTV) string model and subsequently by harmonic gauge fixing the Bandos--Zheltukhin (BZ) model, with constrained spinorial coordinates.