We study an N = (4, 4) supersymmetric gauged linear sigma model which gives rise to the nonlinear sigma model for multi-centered KK-monopoles. We find a new T-duality transformation of the model even in the presence of F-terms. Performing T-duality, we find the gauged linear sigma model whose IR limit describes the exotic 5 2 2 -brane with B-field.

Abstract:We study worldsheet instanton corrections to the exotic 5 2 2 -brane geometry in type II string theory. The BPS vortices in the N = (4, 4) gauged linear sigma model modify the geometry of the 5 2 2 -brane. We find that the modification of the geometry is understood by the localization in the T-dualized winding direction.

We construct world-volume effective actions of exotic 5 2 2 -branes in type IIA and IIB string theories. The effective actions are given in fully space-time covariant forms with two Killing vectors associated with background isometries. The effective theories are governed by the six-dimensional N = (2, 0) tensor multiplet and N = (1, 1) vector multiplet, respectively. Performing the S-duality transformation to the 5 2 2 -brane effective action in type IIB string theory, we also work out the world-volume action of the 5 2 3 -brane. We discuss some additional issues relevant to the exotic five-branes in type I and heterotic string theories.

We study the string worldsheet description of the background geometry of the exotic 5 2 2 -brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic 5 2 2 -brane with a single gauged isometry. The new GLSM with two gauged isometries has only N = (2, 2) supersymmetry rather than N = (4, 4) supersymmetry of the original GLSM. This is caused by a conflict between two different SU(2) R associated with the two gauge symmetries. However, if we take a certain limit, we can find the genuine string sigma model of the background geometry of the exotic 5 2 2 -brane with N = (4, 4) supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic 5 2 2 -brane. The worldsheet instanton corrections to the string sigma model can be traced in terms of the two gauge fields in the new GLSM. This new GLSM gives rise to a different feature of the quantum corrections from the one in the GLSM with the single gauged isometry.

We define the open string version of the nonlinear sigma model on doubled geometry introduced by Hull and Reid-Edwards, and derive its boundary conditions. These conditions include the restriction of D-branes to maximally isotropic submanifolds as well as a compatibility condition with the Lie algebra structure on the doubled space. We demonstrate a systematic method to derive and classify D-branes from the boundary conditions, in terms of embeddings both in the doubled geometry and in the physical target space. We apply it to the doubled three-torus with constant H-flux and find D0-, D1-, and D2-branes, which we verify transform consistently under T-dualities mapping the system to f -, Q-and R-flux backgrounds.We also require the Neumann projector to be integrable, so that it locally defines the brane as a smooth submanifold of the target space,The projectors are moreover required to be orthogonal with respect to the doubled metric M IJ , 0 = Ξ I K M IJ Ξ