Higher derivative corrections to DBI action at $ \alpha'^2$ order
  We use the compatibility of D-brane action with linear off-shell T-duality and linear on-shell S-duality as guiding principles to find all world volume couplings of one massless closed and three massless open strings at order $\alpha'^2$ in type II superstring theories in flat space-time. 
Komeil Babaei Velni and Ali Jalali
hep-th