T-duality transformations for the NS5-brane along angular directions

Understand

In this note we study T-duality transformations for the NS5-brane and its orbifolds along angular directions.

• We identify a geometric charge for these configurations and show that it is interchanged with the H-flux under T-duality.
• We furthermore perform a supersymmetry analysis and find that T-duality can break supersymmetry, in agreement with earlier results in the literature.
• We contrast our findings to compactifications of the NS5-brane on tori, which have vanishing geometric charge and for which T-duality transformations along the compact directions preserve supersymmetry.