 T-duality of D-brane boundary conditions

For a compact string embedding map coordinate, T-duality preserves its left-moving part and reverses its right-moving part. Consequently ${\partial }_{\tau }\tilde{X}={\partial }_{\sigma }X$ and ${\partial }_{\sigma }\tilde{X}={\partial }_{\tau }X$. A Neumann boundary condition becomes a Dirichlet boundary condition and conversely. A D-brane wrapping the circle loses one spatial worldvolume dimension; a D-brane transverse to it gains one in the dual description.