On supersymmetric $D6$-$\bar D 6$ systems with magnetic fields

TL;DR

This paper investigates supersymmetric D6-anti-D6 brane systems with magnetic fields, identifying conditions for stability and supersymmetry preservation, and confirming these through spectrum analysis and interaction amplitude calculations.

Contribution

It establishes explicit conditions for supersymmetry and stability in D6-anti-D6 systems with magnetic fields, aligning spectrum analysis with low-energy effective theory results.

Findings

Conditions for absence of tachyons match low-energy theory predictions.

Identified a four-parameter family of stable, supersymmetric solutions.

Confirmed no-force condition through interaction amplitude calculations.

Abstract

We study systems of $D6$ and $\bar D 6$ branes with non zero world-volume magnetic fields in the weak coupling limit. We find two configurations for which the conditions for absence of tachyons in the spectra coincide exactly with those found in the low energy effective theory approach, for the systems to preserve 1/8 of the supersymmetries of the Type $IIA$ string theory vacuum. These conditions give rise to a four-parameter family of solutions in each case. We present further evidence of the stability of these systems by computing the lowest order interaction amplitude, verifying the no force condition as well as the supersymmetric character of the spectrum.