Kaluza-Klein Monopoles and Gauged Sigma-Models

TL;DR

This paper develops an effective action for eleven-dimensional Kaluza-Klein monopoles using gauged sigma-models, and explores their dimensional reduction, T-duality, and potential connections to M-theory branes.

Contribution

It introduces a novel effective action for Kaluza-Klein monopoles based on gauged sigma-models, linking eleven-dimensional solutions to ten-dimensional branes and dualities.

Findings

Effective action for 11D Kaluza-Klein monopoles proposed.

Dimensional reduction yields D-6-brane effective action.

T-duality relates heterotic monopole to solitonic 5-brane.

Abstract

We propose an effective action for the eleven-dimensional (bosonic) Kaluza-Klein monopole solution. The construction of the action requires that the background fields admit an Abelian isometry group. The corresponding sigma-model is gauged with respect to this isometry. The gauged sigma-model is the source for the monopole solution. A direct (double) dimensional reduction of the action leads to the effective action of a 10-dimensional D-6-brane (IIA Kaluza-Klein monopole). We also show that the effective action of the 10-dimensional heterotic Kaluza-Klein monopole (which is a truncation of the IIA monopole action) is T-dual to the effective action of the solitonic 5-brane. We briefly discuss the kappa-symmetric extension of our proposal and the possible role of gauged sigma-models in connection with the conjectured M-theory 9-brane.