Duality and Weyl Symmetry of 7-brane Configurations

TL;DR

This paper investigates the duality symmetries of 7-brane configurations in string theory, establishing their relation to Weyl reflections and Dynkin diagram symmetries, and computing their duality groups.

Contribution

It defines the duality subgroup of SL(2,Z) for 7-branes and characterizes duality groups via Dynkin diagram symmetries, including affine configurations.

Findings

Duality groups are computed for all localizable 7-brane configurations.

Weyl reflections correspond to brane transpositions exchanging connected branes.

Affine configurations have invariant brane transpositions that act nontrivially on junction charges.

Abstract

Extending earlier results on the duality symmetries of three-brane probe theories we define the duality subgroup of SL(2,Z) as the symmetry group of the background 7-branes configurations. We establish that the action of Weyl reflections is implemented on junctions by brane transpositions that amount to exchanging branes that can be connected by open strings. This enables us to characterize duality groups of brane configurations by a map to the symmetry group of the Dynkin diagram. We compute the duality groups and their actions for all localizable 7-brane configurations. Surprisingly, for the case of affine configurations there are brane transpositions leaving them invariant but acting nontrivially on the charges of junctions.