D-branes in the Euclidean $Ad{S}_3$ and T-duality

Abstract

We show that D-branes in the Euclidean $Ad{S}_3$ can be naturally associated to the maximally isotropic subgroups of the Lu-Weinstein double of SU(2). This picture makes very transparent the residual loop group symmetry of the D-brane configurations and gives also immediately the D-branes shapes and the $\sigma$-model boundary conditions in the de Sitter T-dual of the $SL(2,C)/SU(2)$ WZW model.

29 pages, LaTeX, references added