Superstring in doubled superspace

The covariant and kappa-symmetric action for superstring in direct product of two flat D=10D=10N=1N=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.