Superstring in doubled superspace

The covariant and kappa-symmetric action for superstring in direct product of two flat D=10 N=1 superspaces is presented. It is given by the sum of supersymmetric generalization of two copies of chiral boson actions constructed with the use of the Pasti-Sorokin-Tonin (PST) technique. The chirality of 8 `left' bosons and 8 `left' fermions and the anti-chirality of their `right' counterparts are obtained as gauge fixed version of the equations of motion, so that the physical degrees of freedom are essentially those of the II Green-Schwarz superstring. Our action is manifestly T-duality invariant as the fields describing oscillating and winding modes enter it on equal footing.