The group structure of non-Abelian NS-NS transformations

TL;DR

This paper investigates how non-Abelian NS-NS gauge transformations act on multiple D-branes, revealing a complex interplay with U(N) symmetries and deriving their algebraic structure.

Contribution

It uncovers the non-trivial mixing of NS-NS transformations with U(N) gauge symmetries and computes their algebraic relations and Jacobi identities.

Findings

Pure gauge NS-NS transformations form a U(N) symmetry

Full NS-NS transformations mix with U(N) non-trivially

Derived the algebraic structure and Jacobi identities of combined transformations

Abstract

We study the transformations of the worldvolume fields of a system of multiple coinciding D-branes under gauge transformations of the supergravity Kalb-Ramond field. We find that the pure gauge part of these NS-NS transformations can be written as a U(N) symmetry of the underlying Yang-Mills group, but that in general the full NS-NS variations get mixed up non-trivially with the U(N). We compute the commutation relations and the Jacobi identities of the bigger group formed by the NS-NS and U(N) transformations.