DBI analysis of generalised permutation branes

TL;DR

This paper studies generalized permutation D-branes on product group manifolds in WZNW models, demonstrating they satisfy the Dirac-Born-Infeld equations and extending known constructions to cases with different levels.

Contribution

It provides evidence that generalized permutation D-branes satisfy the DBI equations for arbitrary compact, simply connected Lie groups, extending previous geometric constructions.

Findings

Generalized permutation D-branes satisfy DBI equations for all compact simple Lie groups.

Supports the geometric construction of these D-branes when levels differ.

Extends the understanding of D-branes beyond equal level cases.

Abstract

We investigate D-branes on the product GxG of two group manifolds described as Wess-Zumino-Novikov-Witten models. When the levels of the two groups coincide, it is well known that there exist permutation D-branes which are twisted by the automorphism exchanging the two factors. When the levels are different, the D-brane charge group demands that there should be generalisations of these permutation D-branes, and a geometric construction for them was proposed in hep-th/0509153. We give further evidence for this proposal by showing that the generalised permutation D-branes satisfy the Dirac-Born-Infeld equations of motion for arbitrary compact, simply connected and simple Lie groups G.