Some remarks on defects and T-duality

TL;DR

This paper explores the role of defects in conformal field theories, their relation to T-duality, and geometric structures like Fourier-Mukai transforms, with applications to string theory models.

Contribution

It establishes a connection between defect lines, T-duality, and geometric structures in conformal field theories, including explicit examples involving S^1-fibrations and rational CFTs.

Findings

Relation between Poincare line bundles and T-duality boundary conditions

Diagonal defects induce B-field shifts

Geometric interpretation of T-duality in WZW models

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.