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 KaluzaKlein 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.

We construct the explicit worldvolume effective actions of the type IIB NS-5-brane and KK-monopole. These objects are obtained through a T -duality transformation from the IIA KK-monopole and the IIA NS-5-brane respectively. We show that the worldvolume field content of these actions is precisely that necessary to describe their worldvolume solitons. The IIB NS-5-brane effective action is shown to be related to the D-5-brane's by an S-duality transformation, suggesting the way to construct (p, q) 5-brane multiplets. The IIB KKmonopole is described by a gauged sigma model, in agreement with the general picture for KK-monopoles, and behaves as a singlet under S-duality. We derive the explicit T -duality rules NS-5-brane ↔ KK, which we use for the construction of the previous actions, as well as NS-5 ↔ NS-5, and KK ↔ KK.

We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory.We first consider target-space duality ("T duality") transformations in absence of vector fields. We find that for one isometry the full duality group is (SO ↑ (1, 1)) 3 × D 4 , the discrete part (D 4 ) being non-Abelian. We, then, include non-Abelian Yang-Mills fields and find the corresponding generalization of the T duality transformations. We study the α ′ corrections to these transformations and show that the T duality rules considerably simplify if the gauge group is embedded in the holonomy group.Next, in the case in which there are Abelian vector fields, we consider the duality group that includes the transformation introduced by Sen that rotates among themselves components of the metric, axion and vector field.Finally we list the duality symmetries of the Type II theories with one isometry.

We give a classification of all multiple intersections of D-branes in ten dimensions and M-branes in eleven dimensions that correspond to threshold BPS bound states. The residual supersymmetry of these composite branes is determined. By dimensional reduction composite p-branes in lower dimensions can be constructed. We emphasize in dimensions D ≥ 2 those solutions which involve a single scalar and depend on a single harmonic function. For these extremal branes we obtain the strength of the coupling between the scalar and the gauge field. In particular, we give a D-brane and M-brane interpretation of extreme p-branes in two, three and four dimensions.

We construct a non-Abelian world volume effective action for a system of multiple M-theory gravitons. This action contains multipole moment couplings to the eleven-dimensional background potentials. We use these couplings to study, from the microscopical point of view, giant graviton configurations where the gravitons expand into an M2-brane, with the topology of a fuzzy 2-sphere, that lives in the spherical part of the AdS 7 × S 4 background or in the AdS part of AdS 4 × S 7 . When the number of gravitons is large we find perfect agreement with the Abelian, macroscopical, description of giant gravitons given in the literature.