D-branes (or not) in the non-Abelian T-dual of the SU(2) WZW model

TL;DR

This paper investigates the behavior of D-branes in the non-Abelian T-dual of the SU(2) WZW model, revealing that many branes become non-physical in the dual space, raising questions about the consistency of non-Abelian duality with open strings.

Contribution

It analyzes D-branes in the non-Abelian T-dual of the SU(2) WZW model with an exact CFT description, highlighting issues with brane localization and duality consistency.

Findings

Many D-branes are sent to infinity in the dual space.

The dual theory's boundary conditions are consistent but lead to non-physical brane configurations.

Results suggest potential inconsistencies in applying non-Abelian T-duality to open string setups.

Abstract

Following on from arXiv:1805.03657, we consider open strings in the non-Abelian T-dual of the $SU(2)_k$ WZW model, with respect to the vector $SU(2)$ isometry. Since in this case the dual theory has an exact CFT description, we look at the chiral algebra-preserving D-branes. The general conclusion is that a large set of branes, while consistent boundary conditions on the worldsheet, are sent to infinity in the target space. This suggests inconsistency of the strict non-Abelian duality with open strings, in this case.