Open-string boundary condition in a B-field

For a D-brane in metric $G$, pulled-back B-field $B$ and worldvolume field strength $F$, tangential open-string coordinates obey the mixed condition $G_{ab}{\partial }_{\sigma }{X}^b+(B+2\pi {\alpha }^{\prime }F{)}_{ab}{\partial }_{\tau }{X}^b=0$. Only the gauge-invariant combination $B+2\pi {\alpha }^{\prime }F$ is physical.