Kaluza-Klein Monopoles and Gauged Sigma-Models

TL;DR

The paper introduces an eleven-dimensional Kaluza-Klein monopole effective action modeled as a gauged sigma-model with an Abelian isometry generated by a Killing vector, including a $k^2$ prefactor and a projected metric $\Pi_{\mu\nu}$. It demonstrates that this action acts as the source for the KK monopole, and shows that direct and double dimensional reductions yield the D6-brane action and the KK10A monopole action, respectively, establishing tension relations between the higher- and lower-dimensional objects. It further establishes a T-duality: the 10D heterotic KK monopole is dual to the heterotic solitonic 5-brane, via reductions to nine dimensions that reproduce Buscher-like rules. The study highlights gauged sigma-models as a unifying framework for describing gravitational solitons and their brane interpretations within M-theory, and discusses potential kappa-symmetric extensions and connections to a conjectured M-theory 9-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.

Figures (1)

• Figure 1: Relation between solutions and effective actions of KK monopoles and other extended objects in M theory and type II string theories. Vertical arrows indicate direct dimensional reduction. Vertical dashed lines indicate direct dimensional reduction in the special direction $z$. Oblique arrows indicate double dimensional reduction. Double arrows indicate T duality relations and wiggly lines indicate that the supergravity solutions are identical, although the effective actions are not.