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

We use compatibility of the second fundamental form corrections to DBI action at order $α'^2$ 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 $α'^2$ in type II superstring theories in flat spcetime.

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