An off-shell D-brane action at order $ \alpha'^2$ in flat spacetime

Abstract

We use compatibility of the second fundamental form corrections to DBI action at order $\alpha'^2$ which includes trace of the second fundamental form, with T-duality and with the linear S-duality as guiding principles to find an off-shell D-brane action at order $\alpha'^2$ in type II superstring theories in flat spcetime.