D-branes in the Euclidean $AdS_3$ and T-duality

TL;DR

This paper explores the geometric and symmetry properties of D-branes in Euclidean AdS_3, revealing their relation to isotropic subgroups and their behavior under T-duality transformations.

Contribution

It introduces a novel association between D-branes in Euclidean AdS_3 and maximally isotropic subgroups of the Lu-Weinstein double, clarifying their symmetries and boundary conditions.

Findings

D-branes correspond to maximally isotropic subgroups

Loop group symmetry of D-branes is clarified

Shapes and boundary conditions under T-duality are derived

Abstract

We show that D-branes in the Euclidean $AdS_3$ 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.