Open strings in the system D5/D9

TL;DR

This paper constructs a six-dimensional Lagrangian for twisted open strings between D5 and D9 branes, demonstrating supersymmetry, matching string amplitude calculations, and analyzing the Kaluza-Klein spectrum with magnetic fluxes.

Contribution

It provides the first explicit six-dimensional Lagrangian for D5/D9 open strings, including supersymmetry verification and spectrum analysis with fluxes.

Findings

Lagrangian exhibits N=1 supersymmetry in six dimensions.

Spectrum matches string theory predictions with magnetic fluxes.

Explicit string amplitude checks confirm the Lagrangian's validity.

Abstract

We construct the six-dimensional Lagrangian for the massless twisted open strings with one end-point ending on a stack of D5 and the other on a stack of D9 branes, interacting with the gauge multiplets living respectively on the D5 and D9 branes. It is first obtained by uplifting to six dimensions the four-dimensional Lagrangian of the N=2 hypermultiplet and manifestly exhibits an SU(2) symmetry. We show by an explicit calculation that it is N=1 supersymmetric in six dimensions and then we check various terms of this Lagrangian by computing string amplitudes on the disk. Finally, starting from this Lagrangian and assuming the presence of non-zero magnetic fluxes along the extra compact dimensions, we determine the spectrum of the Kaluza-Klein states which agrees with the corresponding one obtained from string theory in the field theory limit.