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

TL;DR

This paper investigates how T-duality affects NS5-branes along angular directions, revealing changes in geometric charge and supersymmetry, and contrasting uncompactified and compactified cases.

Contribution

It identifies a geometric charge for NS5-branes, analyzes its transformation under T-duality, and compares supersymmetry preservation in different compactification scenarios.

Findings

T-duality exchanges geometric charge and H-flux.

T-duality can break supersymmetry in angular directions.

Uncompactified and compactified NS5-branes behave differently under T-duality.

Abstract

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. This shows that the uncompactified NS5-brane and the compactified-and-smeared solution have different properties and behave differently under T-duality.