Some remarks on defects and T-duality

TL;DR

This work develops a Lagrangian description of conformal defects in two-dimensional theories via bibranes and bundle gerbes, establishing defect equations of motion and a DBI-like action that respects B-field gauge invariance. It demonstrates that T-duality on toroidal backgrounds is realized by Poincaré line bundles and shows that diagonal bibranes can shift the B-field, connecting to Fourier-Mukai-type transformations in geometric language. Extending to SU(2) WZW models and lens spaces, the authors construct and classify several defect families, relate their action on bulk fields to RCFT endomorphisms, and provide a geometric interpretation of these defects as kernels implementing Fourier-Mukai transforms. The results bridge physical defect constructions with derived-category autoequivalences, offering a concrete, calculable framework for T-duality and B-field monodromies in nontrivial fibrations.

Abstract

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 Poincare 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 S^1-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.