The equations of motion for a conformal field theory in the presence of defect lines can be derived from an action that includes contributions from bibranes. For T-dual toroidal compactifications, they imply a direct relation between Poincaré line bundles and the action of T-duality on boundary conditions. We also exhibit a class of diagonal defects that induce a shift of the B-field. We finally study T-dualities for S¹-fibrations in the example of the Wess–Zumino–Witten model on SU(2) and lens spaces. Using standard techniques from D-branes, we derive from algebraic data in rational conformal field theories geometric structures familiar from Fourier–Mukai transformations.