Wrapped D-Branes as BPS Monopoles: The Moduli Space Perspective

TL;DR

This paper analyzes the moduli space of wrapped D6-branes on K3 and T^2, showing they behave as BPS monopoles with a hyper-Kahler metric similar to Euclidean Taub-NUT, with implications for string theory bound states.

Contribution

It derives the hyper-Kahler moduli space metric for wrapped D6-branes as BPS monopoles, extending previous models to include dynamical internal volume moduli.

Findings

Derived the hyper-Kahler metric for wrapped D-brane monopoles.

Connected the results to Kaluza-Klein monopoles and heterotic string bound states.

Extended the Gibbons-Manton Euclidean Taub-NUT metric to this context.

Abstract

We study the four dimensional effective action of a system of D6-branes wrapped on the K3 manifold times a torus, allowing the volume of the internal manifolds to remain dynamical. An unwrapped brane is at best a Dirac monopole of the dual R-R sector field to which it couples. After wrapping, a brane is expected to behave as a BPS monopole, where the Higgs vacuum expectation value is set by the size of the K3. We determine the moduli space of an arbitrary number of these wrapped branes by introducing a time dependent perturbation of the static solution, and expanding the supergravity equations of motion to determine the dynamics of this perturbation, in the low velocity limit. The result is the hyper-Kahler generalisation of the Euclidean Taub-NUT metric presented by Gibbons and Manton. We note that our results also pertain to the behavior of bound states of Kaluza-Klein monopoles and wrapped NS5-branes in the T^4 compactified heterotic string.