4d-Flat Compactifications With Brane Vorticities

We present solutions in six-dimensional gravity coupled to a sigma model, inthe presence of three-brane sources. The space transverse to the branes is acompact non-singular manifold. The example of O(3) sigma model in the presenceof two three-branes is worked out in detail. We show that the four-dimensionalflatness is obtained with a single condition involving the brane tensions,which are in general different and may be both positive, and anothercharacteristic of the branes, vorticity. We speculate that the adjustment ofthe effective four-dimensional cosmological constant may occur through theexchange of vorticity between the branes. We then give exact instanton typesolutions for sigma models targeted on a general K\"ahler manifold, andelaborate in this framework on multi-instantons of the O(3) sigma model. Thelatter have branes, possibly with vorticities, at the instanton positions, thusgeneralizing our two-brane solution.Comment: 8 pages. New references added and minor typos are correcte