Fuzzy Rings in D6-Branes and Magnetic Field Background

TL;DR

This paper explores novel fuzzy ring and sphere solutions in D6-brane backgrounds with magnetic fields, revealing decay processes and the formation of rotating fuzzy rings via dielectric effects.

Contribution

It introduces new nontrivial fuzzy ring and sphere solutions in D6-brane and magnetic field backgrounds using Myers T-dual Born-Infeld action, highlighting decay and formation mechanisms.

Findings

Fuzzy ring solutions have lower energy than fuzzy sphere solutions.

Fuzzy sphere decays into fuzzy ring in D6-brane background.

Rotating fuzzy rings can form from D0-branes in magnetic backgrounds.

Abstract

We use the Myers T-dual nonabelin Born-Infeld action to find some new nontrivial solutions for the branes in the background of D6-branes and Melvin magnetic tube field. In the D6-Branes background we can find both of the fuzzy sphere and fuzzy ring solutions, which are formed by the gravitational dielectric effect. We see that the fuzzy ring solution has less energy then that of the fuzzy sphere. Therefore the fuzzy sphere will decay to the fuzzy ring configuration. In the Melvin magnetic tube field background there does not exist fuzzy sphere while the fuzzy ring configuration may be formed by the magnetic dielectric effect. The new solution shows that $D_0$ propagating in the D6-branes and magnetic tube field background may expand into a rotating fuzzy ring. We also use the Dirac-Born-Infeld action to construct the ring configuration from the D-branes.